2019
6
1
0
95
Optimal Coincidence Best Approximation Solution in bfuzzy Metric Spaces
2
2
In this paper, we prove the existence of optimal coincidence point and best proximity point in bfuzzymetric space for two mappings satisfying certain contractive conditions and prove some proximal theoremswhich provide the existence of an optimal approximate solution to some operator equations which are notsolvable. We also provide an application to the fixed point theory of our obtained results.
1

1
12


Mujahid
Abbas
Department of Mathematics, Government College University,Lahore 54000, Pakistan.
Department of Mathematics, Government College
Iran
abbas.mujahid@gmail.com


N.
Saleem
Department of Mathematics, University of Management and Technology, Lahore, Pakistan
Department of Mathematics, University of
Iran
naeem.saleem2@gmail.com


K.
Sohail
Department of Mathematics, Government College University,Lahore 54000, Pakistan.
Department of Mathematics, Government College
Iran
kinsohail@yahoo.com
Fuzzy metric space
bFuzzy metric space
Optimal approximate solution
Fuzzy expansive
Fuzzy isometry
sincreasing sequence
tnorm
[[1]H. Alolaiyan, N. Saleem, M. Abbas, A natural selection of a graphic contraction transformation in fuzzy metric##spaces, J. Nonlinear Sci. Appl., 11 (2018), 218227.##[2]I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal. Ulianowsk, Gos. Ped. Inst.,##30 (1989), 2637.##[3]S. Czerwik, Contraction mappings in bmetric space, Acta Math. Inf. Univ. Ostraviensis, 1 (1993), 511.##[4]T. Dosenovic, A. Javaheri, S. Sedghi, N. Shobe, Coupled fixed point theorem in bfuzzy metric spaces, NOVI SAD##J. MATH., 47(1) (2017), 7788.##[5]A. George, P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems, 90(3)##(1997), 365368.##[6]M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets, and Systems, 27(3) (1983), 385389.##[7]V. Gregori, A. Sapena, On xedpoint theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 125(2) (2002),##[8]N. Hussain, P. Salimi, V. Parvaneh, Fixed point results for various contractions in parametric and fuzzy bmetric##spaces, J. Nonlinear Sci. Appl., 8 (2015), 719739.##[9]I. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11(5) (1975), 336344.##[10]S. Nadaban, Fuzzy bmetric spaces, International Journal of Computers Communications & Control, 11(2) (2016),##[11]Z. Raza, N. Saleem, M. Abbas, Optimal coincidence points of proximal quasicontraction mappings in nonArchimedean##fuzzy metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 37873801.##[12]N. Saleem, M. Abbas, Z. Raza, Optimal coincidence best approximation solution in nonArchimedean fuzzy metric##spaces, Iranian Journal of fuzzy systems, 13(3) (2016), 113124.##[13]B. Schweizer, A. Sklar, Statistical metric spaces, Pacic J.Math., 10(1) (1960), 313334.##[14]S. Sedghi, N. Shobe, Common fixed point theorems in bfuzzy metric spaces, Nonlinear Function Analysis and##Application, 17(3) (2012), 349359.##[15]L. A. Zadeh, Fuzzy Sets, Informations and control, 8(3) (1965), 338353.##]
A Note on the Solutions of a SturmLiouville Differential Inclusion with "Maxima"
2
2
We consider a boundary value problem associated with a SturmLiouville differential inclusion with "maxima" and we prove a Filippov type existence result for this problem.
1

13
17


Aurelian
Cernea
1Faculty of Mathematics and Informatics, University of Bucharest, Academiei 14, 010014 Bucharest, Romania.
2Academy of Romanian Scientists, Splaiul Independentei 54, 050094 Bucharest, Romania.
1Faculty of Mathematics and Informatics,
Iran
acernea@fmi.unibuc.ro
Boundary value problem
differential inclusion
setvalued mapping
[[1] J.P. Aubin, H. Frankowska, Setvalued Analysis, Birkhauser, Basel, (1990).##[2] D.D. Bainov, S. Hristova, Differential equations with maxima, Chapman and Hall/CRC, Boca Raton, (2011).##[3] A. Cernea, Existence of solutions for a class of functional differential inclusions with "maxima", Fixed Point##Theory, 19 (2018), 503514.##[4] A. Cernea, On a SturmLiouville type functional differential inclusion with "maxima", Adv. Dyn. Syst. Appl., 13##(2018), 101112.##[5] A.F. Filippov, Classical solutions of differential equations with multivalued righthand side, SIAM J. Control, 5##(1967), 609621.##[6] L. Georgiev, V.G. Angelov, On the existence and uniqueness of solutions for maximum equations, Glasnik Mat.,##37 (2002), 275281.##[7] P. Gonzalez, M. Pinto, Convergent solutions of certain nonlinear differential equations with maxima, Math.##Comput. Modelling, 45 (2007), 110.##[8] E.N. Mahmudov, Optimization of Mayer problem with SturmLiouville type differential inclusion, J. Optim.##Theory Appl., 177 (2018), 345375.##[9] M. Malgorzata, G. Zhang, On unstable neutral difference equations with "maxima", Math. Slovaca, 56 (2006),##[10] D. Otrocol, Systems of functional differential equations with maxima, of mixed type, Electronic J. Qual. Theory##Diff. Equations, 2014 (2014), 9 pages.##[11] D. Otrocol, I.A. Rus, Functionaldifferential equations with "maxima" via weakly Picard operator theory, Bull.##Math. Soc. Sci. Math. Roumanie, 51(99) (2008), 253261.##[12] D. Otrocol, I.A. Rus, Functionaldifferential equations with "maxima" of mixed type, Fixed Point Theory, 9##(2008), 207220.##[13] E. P. Popov, Automatic regulation and control, Nauka, Moskow, (1966) (in Russian).##]
Some Notes on the Paper [Further Discussion on Modiﬁed Multivalued α_*ΨContractive Type Mappings]
2
2
In this paper, we show that the claim of the paper [Ali et al., Further discussion on modified multivaluedα_*Ψcontractive type mappings, Filomat 29 (2015)] which says that the notion of α_*ηΨcontractive multivaluedmappings can not be reduced into α_*Ψcontractive multivalued mappings, is not true. Also, weprovide a common fixed point result for an α_*admissible countable family of multivalued mappings. Finally,we show that the common fixed point result of Ali et al. for a countable family of multivalued mappingsusing α_*admissible mappings with respect to η can be reduced to α_*admissible mappings without usingthe auxiliary function].
1

18
22


Babak
Mohammadi
Department of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran.
Department of Mathematics, Marand Branch,
Iran
bmohammadi@marandiau.ac.ir


Vahid
Parvaneh
Department of Mathematics, GilanEGharb Branch, Islamic Azad University, GilanEGharb, Iran
Department of Mathematics, GilanEGharb
Iran
zam.dalahoo@gmail.com
α_*Ψcontractive
α_*ηΨ contractive
Common fixed point
multivalued mapping
[[1]M. U. Ali, T. Kamran, Multivalued F contractions and related fixed point theorems with an application, Filomat,##4 (2016), 37793793.##[2]M. U. Ali, T. Kamran, E. Karapinar, (α,Ψ,ξ)contractive multivalued mappings, Fixed Point Theory Applications,##2014 2014: 7.##[3]M. U. Ali, T. Kamran, E. Karapinar, A new approach to (α,Ψ)contractive nonself multivalued mappings, Journal##Inequalities and Applications, 2014 2014 :71.##[4]M. U. Ali, T. Kamran, On (α_*,Ψ)contractive multivalued mappings, Fixed Point Theory, and Applications,##2013 2013 :137.##[5]M. U. Ali, T. Kamran,W. Sintunavarat, P. Katchang, MizoguchiTakahashis fixed point theorem with α, η functions,##Abstract and Applied Analysis, 2013 (2013), Article ID 418798.##[6]M. U. Ali, T. Kamran, E. Karapinar, Further discussion on modified multivalued α_*Ψcontractive type mappings,##Filomat, 29 (2015), 18931900.##[7]H. Alikhani, Sh. Rezapour, N. Shahzad, Fixed points of a new type of contractive mappings and multifunctions,##Filomat, 27 (2013), 13151319.##[8]P. Amiri, S. Rezapour, N. Shahzad,Fixed points of generalized αΨcontractions, Revista de la Real Academia de##Ciencias Exactas Fisicas y Naturales Serie A Mate doi: 10.1007/s1339801301239.##[9]J. H. Asl, S. Rezapour, N. Shahzad, On fixed points of αΨcontractive multifunctions, Fixed Point Theory and##Applications, 2012 2012 :212.##[10]M. Berzig, E. Karapinar, Note on "Modied αΨ contractive mappings with application", Thai Journal of Mathematics##(2014) In press.##[11]N. Hussain, P. Salimi, A. Latif, Fixed point results for single and setvalued αηΨcontractive mappings, Fixed##Point Theory and Applications, 2013 2013: 212.##[12]E. Karapinar, αΨGeraghty contraction type mappings and some related fixed point results, Filomat, 28 (2014)##[13]E. Karapinar, B. Samet, Generalized αΨcontractive type mappings and related fixed point theorems with applications,##Abstract Applied Analysis, 2012 (2012) Article id: 793486.##[14]G. Minak, I. Altun, Some new generalizations of MizoguchiTakahashi type fixed point theorem, Journal Inequalities##, and Applications, 2013 2013: 493.##[15]B. Mohammadi, S. Rezapour, N Shahzad, Some results on fixed points of αΨCiric generalized multifunctions,##Fixed Point Theory and Applications, 2013 2013: 24.##[16]B. Mohammadi, S. Rezapour, On modified αφcontractions, Journal of Advanced Mathematical Studies, 6 (2013),##[17]P. Salimi, A. Latif, N. Hussain, Modified αΨcontractive mappings with applications, Fixed Point Theory and##Applications, 2013 2013:151.##[18]P. Salimi, C. Vetro, P. Vetro, Fixed point theorems for twisted (α,β)Ψcontractive type mappings and applications,##Filomat, 27 (2013), 605615.##[19]B. Samet, C. Vetro, P. Vetro, Fixed point theorems for αΨcontractive type mappings, Nonlinear Analysis, 75##(2012), 21542165.##]
Fixed Point Theorems for Dislocated Quasi G Fuzzy Metric Spaces
2
2
The aim of this paper is to introduce the new concept of ordered complete dislocated quasi Gfuzzy metricspace. The notion of dominated mappings is applied to approximate the unique solution of nonlinearfunctional equations. In this paper, we nd the fixed point results for mappings satisfying the locallycontractive conditions on a closed ball in an ordered complete dislocated quasi Gfuzzy metric space.
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23
31


M.
Jeyaraman
P.G and Research Department of Mathematics, Raja Doraisingam Govt. Arts College, Sivaganga  630561, Tamil Nadu,
India.
P.G and Research Department of Mathematics,
Iran
jeya.math@gmail.com


D.
Poovaragavan
Department of Mathematics , Govt. Arts College For Women, Sivagangai, India.
Department of Mathematics , Govt. Arts College
Iran
poovaragavan87@gmail.com


S.
Sowndrarajan
P.G and Research Department of Mathematics, Raja Doraisingam Govt. Arts College, Sivaganga  630561, Tamil Nadu,
India.
P.G and Research Department of Mathematics,
Iran
sowndariitm@gmail.com


Saurabh
Manro
Department of Mathematics, Thapar University, Patiala, Punjab, India.
Department of Mathematics, Thapar University,
Iran
sauravmanro@hotmail.com
fixed point
GFuzzy Metric Spaces
closed ball
Dislocated Quasi Metric Spaces
[[1]M. Arshad, A. Shoaib, I. Beg, Fixed point of a pair of contractive dominated mappings on a closed ball in an##ordered complete dislocated metric space, Fixed Point Theory Appl. 2013 (2013) 115, 15 pages.##[2]M. Asadi, E. Karapinar, P. Salimi, A new approach to Gmetric and related fixed point theorems, J. Inequal.##Appl. 2013 (2013) 12 pages.##[3]H. Aydi, N. Bilgili, E. Karapinar, Common fixed point results from quasi metric space to G metric space, J.##Egyptian Math. Soc. 23 (2015).##[4]A. Azam, S. Hussain, M. Arshad, Common fixed points of Kannan type fuzzy mappings on closed balls, Appl.##Math. Inf. Sci. Lett. 1 (2)(2013), 710.##[5]A. Azam, S. Hussain, M. Arshad, Common fixed points of Chatterjea type fuzzy mappings on closed balls, Neural##Comput. Appl. 21 (2012), 5313{5317.##[6]A. Azam, M. Waseem, M. Rashid, Fixed point theorems for fuzzy contractive mappings in quasipseudometric##spaces, Fixed Point Theory Appl. 27 (2013) 14 pages.##[7]H. Hydi, W. Shatanawi, C. Vetro, On generalized weak Gcontraction mappings in Gmetric spaces, Comput.##Math. Appl. 62(2011), 42234229.##[8]M. Jleli, B. Samet, Remarks on Gmetric spaces and fixed point theorems, Fixed Point Theory Appl. 210 (2012).##[9]I. Kramosil and J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika, 11(5) (1975), 336344.##[10]Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2006) 289297.##[11]Z. Mustafa, H. Obiedat, F. Awawdeh, Some fixed point theorem for mappings on a complete Gmetric space,##Fixed Point Theory Appl. 2008 (2008) 12 pages.##[12]H. Obiedat, Z. Mustafa, Fixed point results on a nonsymmetric Gmetric space, Jordan J. Math. Stat. 3 (2010)##M. Jeyaraman, D. Poovaragavan, S. Sowndrarajan, S. Manro, Commun. Nonlinear Anal. 1 (2019), 2331##[13]B. Samet, C. Vetro, F. Vetro, Remarks on Gmetric spaces, Int. J. Anal. 2013 (2013) 6 pages.##[14]A. Shoaib, M. Arshad, J. Ahmad, Fixed point results of locally contractive mappings in ordered quasipartial metric##spaces, Sci. World J. 2013 (2013) 14 pages.##[15]S. Zhou, F. Gu, Some new fixed points in Gmetric spaces, J. Hangzhou Normal University 11 (2010) 4750.##[16]L. A. Zadeh , Fuzzy sets, Inform. and Control, 8 (1965), 338353.##]
On the Zeros of the Polar Derivative of a Polynomial
2
2
Let P(z) be a polynomial of degree n whose coefficients satisfy an ≥ an−1 ≥ ... ≥ a0 > 0.Then according to the EnstromKakeya Theorem, all the zeros of P(z) lie in z≤ 1. Aziz and Mohammad have shown that under the same condition on coeﬃents the zeros of P(z) whose modulus is greater than or equal to n/(n+1) are simple. In this paper, we extend the above result to the polar derivative.
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32
39


M.
Gulzar
Department of Mathematics, University of Kashmir, Srinagar 190006, Jammu & Kashmir, India
Department of Mathematics, University of
Iran
gulzarmh@gmail.com


B.
Zargar
Department of Mathematics, University of Kashmir, Srinagar 190006, Jammu & Kashmir, India
Department of Mathematics, University of
Iran
bazargar@gmail.com


R.
Akhter
Department of Mathematics, University of Kashmir, Srinagar 190006, Jammu & Kashmir, India
Department of Mathematics, University of
Iran
rubiaakhter036@gmail.com
Coeﬃcients
Polynomial
Polar Derivative
[[1]A.Aziz, Q.G.Mohammad, On the zeros of certain class of polynomials and related analytic functions,##J.Math.Anal.Appl.75(1980), 495502.##[2]A.Aziz, Q.G.Mohammad, Zero free regions for polynomials and some generalizations of EnestromKakeya Theorem,##Canad.Math.Bull.27(3),1984, 265272.##[3]S. D. Bairagi, Viny Kumar Jain, T. K. Mishra, L. Saha, On the location of the zeros of certain polynomials,##Publications De L'Institut Mathematique, Nouvelle serie, tome 99(113)(2016)287294.##[4]M. Marden, Geometry of polynomials, Math.Surveys No.3, Amer.Math.Soc., Providence, Rhode Island, 1966.##[5]M. H. Gulzar and A. W. Manzoor, On the zeros of the polar derivative of polynomials, International Journal of##Current Research, 8(2), (2016)2666926674.##[6]M. H. Gulzar and Rubia Akhter, On the location of the zeros of certain polynomials, International Journal of##Advanced Scientific and Technical Research 8(3) (2018) 5461.##[7]G. V. Milovanovic, D. S. Mitrinovic, T. M. Rassias, Topics in polynomials, Extremal problems, Inequalities, Zeros,##World Scientific, SingaporeNew JersyLondonHongkong, 1994.##[8]P.Ramulu and G. L. Reddy, On the zeros of polar derivatives, International Journal of Recent Research in Mathematics,##Computer Science and Information Technology, Vol.2, Issue 1 (April2015September2015), 143145.##[9]G. L. Reddy, P. Ramulu and C. Gangadhar, On the zeros of polar derivative of polynomials, Journal of Research##in Applied Mathematics, 2(4), (2015) 47.##[10]Q. I. Rahman, G. Schmeisser, Analytic Theory Of Polynomials, Oxford University Press, Oxford, 2002.##]
Fixed Points of Almost Geraghty Contraction Type Maps/Generalized Contraction Maps With Rational Expressions in bMetric Spaces
2
2
In this paper, we introduce almost Geraghty contraction type maps for a single self map andprove the existence and uniqueness of ﬁxed points. We extend it to a pair of selfmaps by deﬁningalmost Geraghty contraction type pair of maps in which one of the maps is bcontinuous in acomplete bmetric space. Further, we prove the existence of common ﬁxed points for a pair ofselfmaps satisfying a generalized contraction condition with rational expression in which one ofthe maps is bcontinuous. Our results extend and generalize some of the known results that areavailable in the literature. We draw some corollaries from our results and provide examples insupport of our results.
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40
59


Gutti Venkata
Ravindranadh Babu
Department of Mathematics, Andhra University, Visakhapatnam530 003, India
Department of Mathematics, Andhra University,
Iran
gvr_babu@hotmail.com


Dasari
Ratna Babu
Department of Mathematics, Andhra University, Visakhapatnam530 003, India
Department of Mathematics, Andhra University,
Iran
ratnababud@gmail.com
Common ﬁxed points
bmetric space
bcontinuous
Almost Geraghty contraction type maps
[[1] M. Abbas, G. V. R. Babu, and G. N. Alemayehu, On common ﬁxed points of weakly compatible##mappings satisfying ‘generalized condition (B)’, Filomat 25: 2(2011), 919.##[2] A. Aghajani, M. Abbas and J. R. Roshan, Common ﬁxed point of generalized weak contractive##mappings in partially ordered bmetric spaces, Math. Slovaca, 64(4)(2014), 941960.##[3] H. Aydi, M. F. Bota, E. Karapinar and S. Mitrovic, A ﬁxed point theorem for setvalued quasi##contractions in bmetric spaces, Fixed Point Theory Appl., 88(2012), 8 pages.##[4] G. V. R. Babu, M. L. Sandhya and M. V. R. Kameswari, A note on a ﬁxed point theorem of##Berinde on weak contractions, Carpathia. J. Math., 24(1)(2008), 812.##[5] G. V. R. Babu and P. Sudheer Kumar, Common ﬁxed points of almost generalized (α,ψ,φ,F)contraction##type mappings in bmetric spaces, J. Inter. Math. Virtual Inst., 9(2019), 123137.##[6] I. A. Bakhtin, The contraction mapping principle in almost metric spaces, Func. Anal. Gos. Ped.##Inst. Unianowsk, 30(1989), 2637.##[7] V. Berinde, Approximating ﬁxed points weak contractions using Picard iteration, Nonlinear Anal.##Forum, 9(1)(2004), 4353.##[8] V. Berinde, General contractive ﬁxed point theorems for Cirictype almost contraction in metric##spaces, Carpathia J. Math., 24(2)(2008), 1019.##[9] M. Boriceanu, Strict ﬁxed point theorems for multivalued operators in bmetric spaces, Int. J.##Mod. Math., 4(3)(2009), 285301.##[10] M. Boriceanu, M. Bota, and A. Petrusel, Multivalued fractals in bmetric spaces, Cent. Eur. J.##Math., 8(2)(2010), 367377.##[11] N. Bourbaki, Topologie Generale, Herman: Paris, France, 1974.##[12] S. Czerwik, Contraction mappings in bmetric spaces, Acta Math. Inform. Univ. Ostraviensis,##1(1993), 511.##[13] S. Czerwik, Nonlinear setvalued contraction mappings in bmetric spaces, Atti del Seminario##Matematico e Fisico (DellUniv. di Modena), 46(1998), 263276.##[14] B. K. Dass and S. Gupta, An extension of Banach contraction principle through rational expressions,##Indian J. Pure and Appl. Math., 6(1975), 14551458.##[15] D. Dukic, Z. Kadelburg and S. Radenovic, Fixed points of Geraghtytype mappings in various##generalized metric spaces, Abstr. Appl. Anal.,(2011), Article ID 561245, 13 pages.##[16] H. Faraji, D. Savic, and S. Radenovic, Fixed point theorems for Geraghty contraction type mappings##in bmetric spaces and applications, Axioms, 8(34)(2019), 12 pages.##[17] H. Huang, G. Deng, and S. Radenovic, Fixed point theorems in bmetric spaces with applications##to differential equations, J. Fixed Point Theory. Appl., 2018, 24 pages.##[18] N. Hussain, V. Paraneh, J. R. Roshan and Z. Kadelburg, Fixed points of cycle weakly##(ψ,φ,L,A,B)contractive mappings in ordered bmetric spaces with applications, Fixed Point##Theory Appl., 2013(2013), 256, 18 pages.##[19] M. A. Geraghty, On contractive mappings, Proc. Amer. Math. Soc., 40(1973), 604608.##[20] P. Kumam and W. Sintunavarat, The existence of ﬁxed point theorems for partial qsetvalued##quasicontractions in bmetric spaces and related results, Fixed Point Theory Appl., 2014(2014):##226, 20 pages.##[21] H. Huang, L. Paunovic and S. Radenovic, On some ﬁxed point results for rational Geraghty##contractive mappings in ordered bmetric spaces, J. Nonlinear Sci. Appl., 8(2015), 800807.##[22] N. Hussain, J. R. Roshan, V. Parvaneh and M. Abbas, Common ﬁxed point results for weak##contractive mappings in ordered bdislocated metric spaces with applications, J. Inequal. Appl.,##2013(2013), 486, 21 pages.##[23] R. J. Shahkoohi and A. Razani, Some ﬁxed point theorems for rational Geraghty contractive##mappings in ordered bmetric spaces, J. Inequal. Appl.,2014(1)(373), 23 pages.##[24] W. Shatanawi, Fixed and common ﬁxed point for mappings satisfying some nonlinear contractions##in bmetric spaces, J. Math. Anal., 7(4)(2016), 112.##[25] F. Zabihi and A. Razani, Fixed point theorems for hybrid rational Geraghty contractive mappings##in ordered bmetric spaces, J. Appl. Math., Article ID 929821, 2014, 9 pages.##]
Exact Solutions of Singular IVPs LaneEmden Equation
2
2
In the paper, [A.M. Rismani, H. Monfared, Numerical solution of singular ivps of laneemden type using a modified Legendre spectral method. Applied Mathematical Modelling, 36 (2012), 48304836.], the authors state that exact solutions for the LaneEmden nonlinear differential equation exist only for m = 0,1 (linear cases) and 5 (nonlinear case). While here,we present real exact solutions for m ∈ (3,∞) and complex m ∈ (−∞,3){1}. Some illustratedexamples presented as well.
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60
63


Mehdi
Asadi
Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran
Department of Mathematics, Zanjan Branch,
Iran
masadi.azu@gmail.com
LaneEmden type equations
Singular IVPs
ODE
[[1]A.M. Rismani, H. Monfared, Numerical solution of singular ivps of laneemden type using a modified legendrespectral##method. Applied Mathematical Modelling, 36 (2012), 48304836.##[2]Y. Khan, Z. Svoboda, Z.Smarda, Solving certain classes of LaneEmden type equations using the differential##transformation method. Advances in Difference Equations, 2012(1) (2012), 174. doi:10.1186/168718472012174.##[3]S. Liao, A new analytic algorithm of laneemden type equations. Applied Mathematics and Computation, 142(1)##(2003), 116. doi:10.1016/S00963003(02)009438.##[4]A. Yldrm, T. OZiS. , Solutions of singular ivps of laneemden type by homotopy perturbation method. Physics Letters##A, 369(1) (2007), 7076. doi:10.1016/j.physleta.2007.04.072.##[5]C.M. Bender, K.A. Milton, S.S. Pinsky, L.M. Simmons, A new perturbative approach to nonlinear problems.##Journal of Mathematical Physics, 30(7), (1989) 14471455.##]
Stancu Type of Cheney and Sharma Operators of Pascal Rough Triple Sequences
2
2
In this paper, we introduce a Stancu type extension of the well known Cheney and Sharma operators and also devoted to the definition of new rough statistical convergence with Pascal Fibonacci binomial matrix is given and some general properties of rough statistical convergence are examined. Furthermore, approximation theory worked as a rate of the rough statistical convergence of Stancu type of Cheney and Sharma operators.
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64
77


Nagarajan
Subramanian
Department of Mathematics, Sastra University, India
Department of Mathematics, Sastra University,
Iran
nsmaths@yahoo.com


Ayhan
Esi
Department of Mathematics, Adiyaman University, 02040, Adiyaman, Turkey.
Department of Mathematics, Adiyaman University,
Iran
aesi23@hotmail.com


A.
Indumathi
Department of Mathematics, Sastra University, India
Department of Mathematics, Sastra University,
Iran
aindumathi43@gmail.com
Rough statistical convergence
Korovkin type approximation theorems
Pascal Fibonacci matrix
positive linear operator
Stancu Cheney and Sharma operators
[[1]S. Aytar Rough statistical Convergence, Numer. Funct. Anal. Optimi., 29(3),(2008), 291303.##[2]Bipan Hazarika, N. Subramanian and A. Esi,On rough weighted ideal convergence of triple sequence of Bernstein polynomials,Proceedings of the Jangjeon Mathematical Society, 21(3) (2018), 497506.##[3]A. Esi , On some triple almost lacunary sequence spaces dened by Orlicz functions, Research and Reviews:Discrete Mathematical Structures, 1(2), (2014), 1625.##[4]A. Esi and M. Necdet Catalbas,Almost convergence of triple sequences, Global Journal of Mathematical Analysis,2(1), (2014), 610.##[5]A. Esi and E. Savas, On lacunary statistically convergent triple sequences in probabilistic normed##space,Appl.Math.and Inf.Sci., 9 (5) , (2015), 25292534.##[6]A. Esi, S. Araci and M. Acikgoz, Statistical Convergence of Bernstein Operators, Appl. Math. and Inf.Sci., 10 (6), (2016), 20832086.##[7]A. Esi, S. Araci and Ayten Esi,  Statistical Convergence of Bernstein polynomial sequences, Advances and Applications in Mathematical Sciences, 16 (3), (2017), 113119.##[8]A. Esi, N. Subramanian and Ayten Esi, On triple sequence space of Bernstein operator of rough I convergence PreCauchy sequences,Proyecciones Journal of Mathematics, 36 (4) , (2017), 567587.##[9]A. Esi and N. Subramanian, Generalized rough Cesaro and lacunary statistical Triple dierence sequence spaces inprobability of fractional order defined by Musielak Orlicz function, International Journal of Analysis and##Applications, 16 (1) (2018), 1624.##[10]A. Esi and N. Subramanian, On triple sequence spaces of Bernstein operator of X3 of rough λstatistical convergence in probability of random variables defined by MusielakOrlicz function, Int. J. open problems Compt.Math, 11 (2) (2019), 6270.##[11]A. J. Dutta A. Esi and B.C. Tripathy,Statistically convergent triple sequence spaces defined by Orlicz function, Journal of Mathematical Analysis, 4(2), (2013), 1622.##[12]S. Debnath, B. Sarma and B.C. Das ,Some generalized triple sequence spaces of real numbers, Journal of nonlinear analysis and optimization, Vol. 6, No. 1 (2015), 7179.##[13]H.Fast, Sur la convergence statistique, Colloq. Math. 2 (1951) 241244.##[14]P.K.Kamthan and M.Gupta, Sequence spaces and series, Lecture notes, Pure and Applied Mathematics, 65 Marcel Dekker, In c., New York , 1981.##[15]S.K. Pal, D. Chandra and S. Dutta Rough ideal Convergence, Hacee. J. Math. and Stat., 42(6),(2013), 633640.##[16]H.X. Phu Rough convergence in normed linear spaces, Numer. Funct. Anal. Optimi., 22,(2001), 201224.##[17]A. Sahiner, M. Gurdal and F.K. Duden, Triple sequences and their statistical convergence, Selcuk J. Appl. Math., 8 No. (2)(2007), 4955.##[18]A. Sahiner, B.C. Tripathy , Some I related properties of triple sequences, Selcuk J. Appl. Math., 9 No. (2)(2008),918.##[19]N. Subramanian and A. Esi, The generalized tripled difference of X3 sequence spaces, Global Journal of Mathematical Analysis, 3 (2) (2015), 5460.##[20]N. Subramanian and A. Esi, On triple sequence space of Bernstein operator of Χ 3 of rough λstatistical convergence in probability definited by MusielakOrlicz function pmetric, Electronic Journal of Mathematical Analysis and Applications, 6 (1) (2018), 198203.##[21]N. Subramanian, A. Esi and M. Kemal Ozdemir, Rough Statistical Convergence on Triple Sequence of Bernstein Operator of Random Variables in Probability, Songklanakarin Journal of Science and Technology, in press(2018)##[22]N. Subramanian, A. Esi and V.A. Khan, The Rough Intuitionistic Fuzzy Zweier Lacunary Ideal Convergence of Triple Sequence spaces, journal of mathematics and statistics, 14 (2018), 7278.##[23]S. Velmurugan and N. Subramanian, Bernstein operator of rough λstatistically and ρCauchy sequences convergence##on triple sequence spaces, Journal of Indian Mathematical Society, 85 (12) (2018), 257265.##[24]H.Steinhaus Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951) 7374.##]
A PredictorCorrector Method for Fractional DelayDifferential System with Multiple Lags
2
2
The purpose of this work is to present numerical solutions of variableorder fractional delay differential equations with multiple lags based on the AdamsBashforthMoulton method, where the derivative is defined in the Caputo variableorder fractional sense. Since the variableorder fractional derivatives contain classical and fractional derivatives as special cases and also single delay is a special case of multiple delays, several results of references are significantly generalized. The error analysis for this method is given and the effectiveness of the algorithm is highlighted with numerical examples.
1

78
88


Salem
Abdelmalek
Department of mathematics, University of Tebessa 12002 Algeria.
Department of mathematics, University of
Iran
salem.abdelmalek@univtebessa.dz


Redouane
Douaifia
Laboratory of Mathematics, Informatics and Systems (LAMIS), Larbi Tebessi University – Tebessa
Laboratory of Mathematics, Informatics and
Iran
redouane.douaifia@univtebessa.dz
variableorder fractional calculus
Delay Differential Equations
Adams BashforthMoulton method
[[1]C. F. Coimbra, Mechanics with variableorder differential operators, Annalen der Physik, 12 (2003), 692703.##[2]K. Diethelm, N. J. Ford, A. D. Freed, A predictorcorrector approach for the numerical solution of fractional differential equations, Nonlinear Dynamics, 29 (2002), 322.##[3]L. Debnath, Recent applications of fractional calculus to science and engineering, International Journal of Mathematics and Mathematical Sciences, 2003 (2003), 34133442.##[4]I. Epstein, Y. Luo, Differential delay equations in chemical kinetics. Nonlinear models: The crossshaped phase diagram and the Oregonator, The Journal of chemical physics, 95 (1991), 244254.##[5]E. Fridman, L. Fridman, E. Shustin, Steady modes in relay control systems with time delay and periodic disturbances, Journal of Dynamic Systems, Measurement, and Control, 122 (2000), 732737.##[6]Y. Kuang, Delay Differential Equations with Applications in Population Biology, Academic Press, Boston, San Diego, New York, (1993).##[7]M. Okamoto, K. Hayashi, Frequency conversion mechanism in enzymatic feedback systems, Journal of theoretical biology, 108 (1984), 529537.##[8]I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, (1999).##[9]S. G. Samko, B. Ross, Integration and differentiation to a variable fractional order, Integral transforms and special functions, 1 (1993), 277300.##[10]S. G. Samko, Fractional integration and differentiation of variable order, Analysis Mathematica, 21 (1995), 213236.##[11]H.Sun, W. Chen, Y. Q. Chen, Variableorder fractional differential operators in anomalous diffusion modeling,Physica A: Statistical Mechanics and its Applications, 388 (2009), 45864592.##[12]H. Sun, W. Chen, H. Sheng, Y. Q. Chen, On mean square displacement behaviors of anomalous diffusions with variable and random orders, Physics Letters A, 374 (2010), 906910.##[13]N. H. Sweilam, A. M. Nagy, T. A. Assiri, N. Y. Ali, Numerical Simulations For VariableOrder Fractional##Nonlinear Delay Differential equations, Journal of Fractional Calculus and Applications, 6 (2015), 7182.##[14]H. Sheng, Y. Chen, T. Qiu, Fractional processes and fractionalorder signal processing: techniques and applications, Springer Science & Business Media, (2011).##[15]D. R. Wille, C. T. Baker, DELSOL{a numerical code for the solution of systems of delaydierential equations, Applied numerical mathematics, 9 (1992), 223234.5.##[16]L. C. Davis, Modications of the optimal velocity traffic model to include delay due to driver reaction time, Physica A: Statistical Mechanics and its Applications, 319 (2003), 557567.##[17]C. F. Lorenzo, T. T. Hartley, Variable order and distributed order fractional operators, Nonlinear dynamics, 29 (2002), 5798.##[18]H. G. Sun, W. Chen, H. Wei, Y. Q. Chen, A comparative study of constantorder and variableorder fractional models in characterizing memory property of systems, The European Physical Journal Special Topics, 193 (2011),185.##[19]L. Galue, S. L. Kalla, B. N. AlSaqabi, Fractional extensions of the temperature eld problems in oil strata, Applied Mathematics and Computation, 186 (2007), 3544.##[20]B. P. Moghaddam, S. Yaghoobi, J. T. Machado, An extended predictorcorrector algorithm for variableorder fractional delay differential equations, Journal of Computational and Nonlinear Dynamics, 11 (2016), 061001.##[21]F. K. Keshi, B. P. Moghaddam, A. Aghili, A numerical technique for variableorder fractional functional nonlinear dynamic systems, International Journal of Dynamics and Control, (2019), 18.##]
A Relation Theoretic Approach for φFixed Point Result in Metric Space with an Application to an Integral Equation
2
2
In this paper, we prove the existence and uniqueness of φfixed point for (F,φ,θ)contraction mapping in a complete metric space with a binary relation. Here the contractive condition is required to hold only forthose elements that are related under the binary relation and not for the whole space. An application isgiven to show the φusability of our result obtained.
1

89
95


D.
Gopal
Department of Applied Mathematics & Humanities, S. V. National Institute of Technology, Surat395007, Gujarat, India
Department of Applied Mathematics & Humanities
Iran
gopal.dhananjay@rediffmail.com


L. M.
Budhia
Department of Applied Mathematics & Humanities, S. V. National Institute of Technology, Surat395007, Gujarat, India
Department of Applied Mathematics & Humanities
Iran
lokesh86budhia@gmail.com


S.
Jain
Poornima College of Engineering, Jaipur302022, Rajasthan, India
Poornima College of Engineering, Jaipur302022,
Iran
shilpi.jain1310@gmail.com
binary relation
φfixed point
(F
φ
θ) contraction
integral equation
[[1]A. Alam and M. Imdad, Relationtheoretic contraction principle. Journal of Fixed Point Theory and Applications, 17(4) (2015), 693702.##[2]A. Sahin, Z. Kalkan, H. Arisoy, On the solution of a nonlinear Volterra integral equation with delay, Sakarya University Journal of Science, 21 (6), 2017, 13671376, doi: 10.16984/saufenbilder.305632.##[3]S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales. Fund.Math. 3 (1922), 13 3181.1##[4]M. Jleli, B. Samet, C. Vetro, Fixed point theory in partial metric spaces via φfixed point's concept in metric spaces, Journal of Inequalities and Applications, 2014 (2014) 426.##[5]P. Kumrod, and W. Sintunavarat, A new contractive condition approach to φfixed point results in metric spaces and its applications. Journal of Computational and Applied Mathematics 311 (2017) , 194204.##[6]M. A. Kutbi, A. Roldan, W. Sintunavarat, J. MartinezMoreno and C. Roldan, Fclosed sets and coupled fixed point theorems without the mixed monotone property. Fixed Point Theory and its Applications, 2013 (2013),doi:10.1186/168718122013 330, 11 pp.1.4 ##[7]S. Lipschutz, Schaums Outlines of Theory and Problems of Set Theory and Related Topics. McGrawHill, New York, 1964.1##[8]A.M. Rismani, H. Monfared, Numerical solution of singular ivps of laneemden type using a modiffed legendrespectral##method. Applied Mathematical Modelling, 36 (2012), 48304836.##[9]Y. Khan, Z. Svoboda, Z. Smarda, Solving certain classes of laneemden type equations using the differential transformation method. Advances in Dierence Equations, 2012(1) (2012), 174. doi:10.1186/168718472012174.##[10]S. Liao, A new analytic algorithm of laneemden type equations. Applied Mathematics and Computation, 142(1)(2003), 116. doi:10.1016/S00963003(02)009438.##[11]A. Yldrm, T.##OZiS. , Solutions of singular ivps of laneemden type by homotopy perturbation method. Physics Letters##A, 369(1) (2007), 70{76. doi:10.1016/j.physleta.2007.04.072.##[12]C.M. Bender, K.A. Milton, S.S. Pinsky, L.M. Simmons, A new perturbative approach to nonlinear problems. Journal of Mathematical Physics, 30(7), (1989) 14471455.##]