ORIGINAL_ARTICLE
Nash equilibrium strategy for two-person zero-sum matrix games on credibility space
In this paper, firstly, we obtain the credibility measure of fuzzy trapezoidal variables. Also, we attain theexpected value of fuzzy trapezoidal variables. Then, based on these theorems, we present the expectedvalue Nash equilibrium strategy of the fuzzy games. In other words, we extend the expected model to fuzzytrapezoidal variables and improve the previous researches in this area. However, in some cases, the gamedoesn't have the Nash equilibrium strategy. Therefore, we investigate the existence of Pareto Nash equilibriumand weak Pareto Nash equilibrium strategies in these cases.
https://www.cna-journal.com/article_89284_352a4f458d1e3b415a27b051b7fb7f83.pdf
2018-06-01
1
7
Matrix game
fuzzy payoffs
Nash equilibrium
fuzzy trapezoidal variables
Somayeh
Haghayeghi
s.haghayeghi@kiau.ac.ir
1
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
LEAD_AUTHOR
Fatemeh
Madandar
fatemeh.madandar@kiau.ac.ir
2
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
AUTHOR
L. Baoding, L. Yian-Kui, Expected value of fuzzy variable and fuzzy expected value models, IEEE Transactions on
1
Fuzzy Systems, 10 (2002), 445-450.
2
[2]B. Dutta, S. K. Gupta, On Nash equilibrium strategy of two-person zero-sum games with trapezoidal fuzzy payffs,
3
Fuzzy Inf. Eng., 6 (2014), 299-314.
4
[3]L. Cunlin, Z. Qiang, Nash equilibrium strategy for fuzzy non-cooperative games, Fuzzy Sets and Systems., 176
5
(2011), 46-55.
6
[4]D. Jian, L. Cun-lin, Z. Gao-sheng, Two-person zero-sum matrix games om credibility space, 2011 Eighth International
7
Conference on Fuzzy Systems and Knowledge Discovery (FSKD).
8
[5]D. Dubios, H. Prade, Possibility theory, Plenum Press, New York, (1988).
9
[6]B. Liu, Uncertain programming, Wiley, New York, (1999).
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[7]B. Liu, Uncertainty theory, Springer-Verlag, Berlin, (2007).
11
[8]T. Maeda, On characterization of equilibrium strategy of bimatrix games with fuzzy payoffs, J. Math. Anal. Appl,
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251 (2000), 885-896.1
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[9]J. von Neumann, O. Morgenstern, Theory of games and economic behavior, Princeton University Press, Princeton,
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New Jersey, (1944).1
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[10]J. Nash, Non-cooperative games, Ann. of Math., 54 (1951), 286-295.
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[11]Martin J. Osborne , A. Rubinstein, A Course in game theory, MIT Press, Cambridge, MA, (1994).1
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[12]M. Sakawa, Fuzzy Sets and Interactive Multiobjective Optimization, Plenum Press, New York, (1993).
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[13]A. V. Yazenin, Fuzzy and stochastic programming, Fuzzy Sets and Systems, 22 (1987), 171-180.
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[14]A. V. Yazenin, On the problem of possibilistic optimization, Fuzzy Sets and Systems, 81 (1996), 133-140.
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[15]L. A. Zadeh, Fuzzy set as a basis for a theory of possibility, Fuzzy Sets and Systems, 1 (1978), 3-28.
21
[16]H. J. Zimmermann, Application of fuzzy set theory to mathematical programming, Inform. Sci., 36 (1985), 29-58.
22
ORIGINAL_ARTICLE
On the existence and global structure of solutions for a class of fractional feedback control systems
In this paper, using topological tools, guiding functions and bifurcation theory, we deal with the existenceof a connected subset of nontrivial solutions of a system whose dynamics of the system and feedback laware expressed in the form of fractional differential equations.
https://www.cna-journal.com/article_89285_c3463b8a684f34eb7cffa4ecb1fb0ada.pdf
2018-06-01
8
18
bifurcation theory
Boundary value problem
Caputo derivative
degree theory
Fredholm operators
guiding functions
Hero
Salahifard
salahifard@gmail.com
1
Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran.
LEAD_AUTHOR
[1] Z. Denkowski, S. Migorski, N. S. Papageorgiou, An Introduction to Nonlinear Analysis: Theory, Kluwer Academic
1
Publishers, Boston, MA, (2003).
2
[2] L. Gorniewicz, Topological Fixed Point Theory of Multivalued Mappings, Topological Fixed Point Theory and Its
3
Applications, second edition, Springer, Dordrecht, (2006).
4
[3] D. D. Haroske, H. Triebel, Distributions, Sobolev Spaces, Elliptic Equations, EMS Textbooks in Mathematics.
5
European Mathematical Society (EMS), Zurich, (2008).
6
[4] Ph. Hartman, Ordinary Differential Equations, Corrected reprint of the second (1982) edition Birkhauser, Boston,
7
MA, Classics in Applied Mathematics, 38, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, (2002).
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[5] D. M. Hyman, On decreasing sequences of compact absolute retracts, Fund. Math., 64 (1969), 91-97.
9
[6] M. Kamenskii, V. Obukhovskii, P. Zecca, Condensing Multivalued Maps and Semilinear Differential Inclusions
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in Banach Spaces, de Gruyter Series in Nonlinear Analysis and Applications, 7, Walter de Gruyter Co., Berlin,
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(2001).
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[7] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland
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Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, (2006).
14
[8] M. A. Krasnoselskii, P. P. Zabreiko, Geometrical Methods of Nonlinear Analysis., Translated from the Russian by
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Christian C. Fenske. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical
16
Sciences], 263. Springer-Verlag, Berlin, (1984).
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[9] W. Kryszewski, Homotopy Properties of Set-valued Mappings, Nicolaus Copernicus University Press, Torun,
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[10] N. V. Loi, V. Obukhovskii, On global bifurcation of periodic solutions for functional differential inclusions, Funct.
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Differ. Equ., 17 (2010), 157-168.
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[11] N. V. Loi, Global behavior of solutions to a class of feedback control systems, Res. Commun. Math. Sci., 2 (2013),
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[12] N. V. Loi, V. Obukhovskii, On the existence of solutions for a class of second-order differential inclusions and
22
applications, J. Math. Anal. Appl., 385 (2012), 517-533.
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[13] N. V. Loi, V. Obukhovskii, P. Zecca, On the global bifurcation of periodic solutions of differential inclusions in
24
Hilbert spaces, Nonlinear Anal., 76 (2013), 80-92.
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[14] V. Obukhovskii, N. V. Loi, S. Kornev, Existence and global bifurcation of solutions for a class of operator-differential inclusions, Dier. Equ. Dyn. Syst., 20 (2012), 285-300.
26
ORIGINAL_ARTICLE
Solvability and asymptotic stability of a class of nonlinear functionalintegral equation with feedback control
Using the technique of measure of noncompactness we prove the existence, asymptotic stability and globalattractivity of a class of nonlinear functional-integral equation with feedback control. We will also includea class of examples in order to indicate the validity of the assumptions.
https://www.cna-journal.com/article_89404_e59d36c95cafd16f5c36a528209f5253.pdf
2018-06-01
19
27
Functional integral equation
Measure of noncompactness
asymptotic stability
Feedback Control
xed point
Payam
Nasertayoob
nasertayoob@aut.ac.ir
1
Department of Mathematics and Computer Science, Amirkabir University of Technology (Polytechnic), Hafez Ave., P. O. Box 15914, Tehran, Iran.
LEAD_AUTHOR
[1] I. K. Aregon, Quadratic equations and applications to Chandrasekhar's and related equations, Bull. Austral. Math. Soc.,
1
32 (1985), 275-292.
2
[2] J. Banas, Measure of noncompactness in the space of continuous temperate functions, Demonstratio Math., 14 (1981), 127-133.
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[3] J. Banas, B. C. Dhage, Global asymptotic stability of solutions of a functional integral equation, Nonlinear Anal., 69 (2008), 1945-1952.
4
[4] J. Banas, K. Goebel, Measure of noncompactness in the Banach space. Lecture Notes in Pure and Applied Mathematics, vol. 60. New York:Dekker, (1980).
5
[5] J. Banas, B. Rzepka, On existance and asymptotic stability of solutions of a nonlinear integral equation, J. Math. Anal. Appl., 284 (2003), 165-173.
6
[6] J. Banas, B. Rzepka, An application of a measure of noncompactness in the study of asymptotic stability, App. Math. Lett., 16 (2003), 1-6.
7
[7] J. Banas, B. Rzepka, On local attractivity and asymptotic stability of solutions of a quadratic Volterra integral equation,
8
Appl. Math. Comput., 213 (2009), 102-111.
9
[8] J. Banas, D. O'Regan, On existence and local attractivity of solutions of a quadratic Volterra integral equation of fractional order, J. Math. Anal. Appl., 34 (2008), 573-582.
10
[9] F. Chen, The permanence and global attractivity of Lotka-Volterra competition system with feedback control, Nonlinear
11
Anal., 7 (2006), 133-143.
12
[10] K. Deimling, Nonlinear Functional analysis, Springer-Verlag, Berlin, (1985). 1
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[11] Z. Liu, S. M. Kang, J. S. Ume, Solvability and asymptotic stability of a nonlinear functional-integral equation, App. Math. Lett., 24 (2011), 911-917.
14
ORIGINAL_ARTICLE
Solutions for some nonlinear functionalintegral equations with applications
In the present manuscript, we prove some results concerning the existence of solutions for some nonlinearfunctional-integral equations which contains various integral and functional equations that considered innonlinear analysis and its applications. By utilizing the techniques of noncompactness measures, we operatethe fixed point theorems such as Darbo's theorem in Banach algebra concerning the estimate on the solutions.The results obtained in this paper extend and improve essentially some known results in the recent literature.We also provide an example of a nonlinear functional-integral equation to show the ability of our main result.
https://www.cna-journal.com/article_89408_99136768161f70d46e04a470fca34827.pdf
2018-06-01
28
39
Banach algebra
Fixed point
Functional-integral equation
Measure of noncompactness
Animesh
Gupta
dranimeshgupta10@gmail.com
1
Department of Mathematics & Computer Science, R.D.V.V. Jabalpur (M.P.) India.
LEAD_AUTHOR
[1] J. Banas, K. Goebel, Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Applied Mathematics,
1
60, Marcel Dekker, New York, (1980).
2
[2] J. Banas, M. Lecko, Fixed points of the product of operators in Banach algebra, Panamer. Math. J., 12 (2002),
3
[3] J. Banas, M. Mursaleen, Sequence spaces, and measures of noncompactness with applications to differential and
4
integral equations, Springer, New York, (2014).
5
[4] J. Banas, B. Rzepka, An application of a measure of noncompactness in the study of asymptotic stability, Appl.
6
Math. Lett., 16 (2003), 1-6.
7
[5] J. Banas, B. Rzepka, On existence and asymptotic stability of solutions of a nonlinear integral equation, J. Math.
8
Anal. Appl., 284 (2003), 165-173.
9
[6] J. Banas, B. Rzepka, On local attractivity and asymptotic stability of solutions of a quadratic Volterra integral
10
equation, Appl. Math. Comput., 213 (2009), 102-111.
11
[7] J. Banas, K. Sadarangani, Solutions of some functional-integral equations in Banach algebra, Math. Comput.
12
Modeling, 38 (2003), 245-250.
13
[8] S. Chandrasekhar, Radiative Transfer, Oxford Univ Press, London, (1950).
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[9] B. C. Dhage, On {condensing mappings in Banach algebras, Math. Student, 63 (1994), 146-152.
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[10] D. Guo, V. Lakshmikantham, X. Z. Liu, Nonlinear Integral Equations in Abstract Spaces, Kluwer, Dordrecht,
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[11] S. Hu, M. Khavani, W. Zhuang, Integral equations arising in the kinetic theory of gases, Appl. Anal., 34 (1989),
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[12] K. Maleknejad, R. Mollapourasl, K. Nouri, Study on existence of solutions for some nonlinear functional integral
18
equations, Nonlinear Anal., 69 (8) (2008), 2582-2588.
19
[13] K. Maleknejad, K. Nouri, R. Mollapourasl, Existence of solutions for some nonlinear integral equations, Commun.
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Nonlinear Sci. Numer. Simul., 14 (2009), 2559-2564.
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[14] K. Maleknejad, K. Nouri, R. Mollapourasl, Investigation on the existence of solutions for some nonlinear
22
functional- integral equations, Nonlinear Anal., 71 (2009), 1575-1578.
23
[15] J. J. Nieto, R. Rodriguez-Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary
24
differential equations, 22 (2005), 223-239.
25
[16] J. J. Nieto, R. Rodriguez-Lopez, Existence and uniqueness of fixed point in partially ordered sets and applications
26
to ordinary differential equations, Acta Math. Sin.(Engl. Ser.), 23 (2007), 2205-2212.
27
[17] A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix
28
equations, Proc. Amer. Math. Soc., 132 (2004), 1435-1443.
29
[18] B. Samet, C. Vetro, Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially
30
ordered metric spaces, Nonlinear Anal., 74 (2011), 4260-4268.
31
ORIGINAL_ARTICLE
Suzuki type common fixed point theorems for four maps using a-admissible in partial ordered complex partial metric spaces
In this paper, we obtain Suzuki type common fixed point theorems for four maps using -admissible inpartial ordered complex partial metric spaces. Also, we give examples to illustrate our theorems.
https://www.cna-journal.com/article_89281_11371c55a67aca6fd49baac8655c1733.pdf
2018-06-01
40
54
Complex partial metric space
a-admissible maps
p_c^*-compatible maps
K. P. R.
Rao
kprrao2004@gmail.com
1
Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar-522510., A.P., India.
LEAD_AUTHOR
A.
Sombabu
somu.mphil@gmail.com
2
Department of Mathematics, NRI Institute of Technology, Agiripalli-521211, A.P., India.
AUTHOR
[1] M. Abbas, M. Arshad, A. Azam, Fixed points of asymptotically regular mappings in complex valued metric spaces,
1
Georgian Math. J., 20 (2013), 213-221.
2
[2] M. Abbas, Y. J. Cho, T. Nazir, Common fixed points of Ciric-type contractive mappings in two ordered generalized
3
metric spaces, Fixed Point Theory Appl., 2012 (2012), 17 pages.
4
[3] M. Abbas, B. Fisher, T. Nazir, Well-posedness and periodic point property of mappings satisfying a rational
5
inequality in an ordered complex valued metric spaces, Sci. Stud. Res. Ser. Math. Inform., 22 (2012), 5-24.
6
[4] M. Abbas, T. Nazir, S. Radenovic, Common fixed points of four maps in partially ordered metric spaces, Appl.
7
Math. Lett., 24 (2011), 1520-1526.
8
K. P. R. Rao, A. Sombabu, Commun. Nonlinear Anal. 5 (2018), 40-54.
9
[5] T. Abdeljawad, Meir-Keeler α-contractive fixed and common fixed point theorem, Fixed Point Theory Appl., 2013
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(2013), 10 pages.
11
[6] I. Altun, A. Erduran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory
12
Appl., 2011 (2011), 10 pages.
13
[7] I. Altun, F. Sola, H. Simsek, Generalized contractions on partial metric spaces, Topology Appl., 157 (2010),
14
2778-2785.
15
[8] H. Aydi, Fixed point results for weakly contractive mappings in ordered partial metric spaces, J. Adv. Math. Stud.,
16
4 (2011), 1-12.
17
[9] A. Azam, B. Fisher, M. Khan, Common fixed point theorems in complex valued metric spaces, Numer. Funct.
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Anal. Optim., 32 (2011), 243-253.
19
[10] S. Banach, Surles operations densles ensembles abstracts.et leur application aux equations integrals, Fund. Math.,
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3 (1922), 133-181.
21
[11] S. Chandok, D. Kumar, Some common fixed point results for rational type contraction mappings in complex valued
22
metric spaces, J. Operators, 2013 (2013), 6 pages.
23
[12] P. Dhivya, M. Marudai, Common fixed point theorems for mappings satisfying a contractive condition of rational
24
expression on an ordered complex partial metric space, Cogent Math., 4 (2017), 10 pages.
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[13] E. Karapinar, Generalizations of Caristi Kirk's Theorem on Partial metric spaces, Fixed Point Theory Appl.,
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2011 (2011), 7 pages.
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[14] E. Karapinar, I. M. Erhan, Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett., 24
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(2011), 1894-1899.
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[15] E. Karapinar, P. Kumam, P. Salimi, On a-Ψ-Meir-Keeler contractive mappings, Fixed Point Theory Appl., 2013
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(2013), 12 pages.
31
[16] C. Klin-eam, C. Suanoom, Some common fixed point theorems for generalized contractive type mappings on
32
complex valued metric spaces, Abstr. Appl. Anal., 2013 (2013), 6 pages.
33
[17] M. Kumar, P. Kumar, S. Kumar, Common fixed point theorems in complex valued metric spaces, J. Ana. Num.
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Theor. 2 (2014), 103-109.
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[18] D. Ilic, V. Pavlovic, V. Rakocevic, Some new extensions of Banach's contraction principle to Partial metric
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spaces, Appl. Math. Lett., 24 (2011), 1326-1330.
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[19] S. G. Matthews, Partial metric topology, Papers on general topology and applications (Flushing, NY, 1992), Ann.
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New York Acad. Sci., 1994 (1994), 183-197.
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[20] H. K. Nashine, M. Imdad, M. Hasan, Common fixed point theorems under rational contractions in complex valued
40
metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 42-50.
41
[21] J. J. Nieto, R. Rodriguez-Lopez, Contractive mapping theorems in partially ordered sets and applications to
42
ordinary dierential equations, Order, 22 (2005), 223-239.
43
[22] J. J. Nieto, R. Rodrguez-Lopez, Existence and Uniqueness of fixed point in partially ordered sets and applications
44
to ordinary differential equations, Acta Math. Sin. (Engl. Ser.), 23 (2007), 2205-2212.
45
[23] A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix
46
equations, Proc. Amer. Math. Soc., 132 (2004), 1435-1443.
47
[24] K. P. R. Rao, G. N. V. Kishore, A unique common fixed point theorem for four maps under ϕ-contractive
48
condition in partial metric spaces, Bull. Math. Anal. Appl., 3 (2011), 56-63.
49
[25] K. P. R. Rao, V. C. C. Raju, P. Ranga Swamy, S. Sadik, Common coupled fixed point theorems for four maps
50
using a-admissible functions in complex-valued b-metric spaces, Int. J. Pure Appl. Math., 108 (2016), 751-766.
51
[26] K. P. R. Rao, P. Ranga Swamy, M. Imdad, Suzuki type unique common fixed point theorems for four maps using
52
a-admissible functions in ordered partial metric spaces, J. Adv. Math. Stud., 9 (2016), 265-277.
53
[27] K. P. R. Rao, P. Ranga Swamy, S. Sadik, E. Taraka Ramudu, Suzuki type common fixed point theorems for four
54
maps using -admissible functions in partial ordered complex valued metric spaces, J. Prog. Res. Math., 7 (2016),928-939.
55
[28] K. P. R. Rao, K. R. K. Rao, V. C. C. Raju, A Suzuki type unique common coupled fixed point theorem in metric
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spaces, Int. J. Inn. Res. Sci. Eng. Tech., 2 (2013), 5187-5192.
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Appl., 64 (2012), 1866-1874.
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[30] B. Samet, M. Rojovic, R. Lazovic, R. Stojiljkovic, Common fixed point results for non-linear contractions in
60
ordered partial metric spaces, Fixed Point Theory Appl., 2011 (2011), 14 pages. 2
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(2012), 2154-2165.
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64
type mappings with applications, Bull. Belg. Math. Soc. Simon Stevin, 22 (2015), 299-318.
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Soc., 24 (2016), 402-409.
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[34] W. Sintunavarat, P. Kumam, Generalized common xed point theorems in complex valued metric spaces and
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applications, J. Inequal. Appl., 2012 (2012), 12 pages.
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K. P. R. Rao, A. Sombabu, Commun. Nonlinear Anal. 5 (2018), 40-54.
70
[35] K. Sitthikul, S. Saejung, Some fixed points in complex valued metric spaces, Fixed Point Theory Appl., 2012
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(2012), 11 pages.
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Soc., 136 (2008), 1861-1869.
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J. Math. Comput. Sci., 6 (2013), 18-26.
77