Stancu Type of Cheney and Sharma Operators of Pascal Rough Triple Sequences

Document Type : Original Article

Authors

1 Department of Mathematics, Sastra University, India

2 Department of Mathematics, Adiyaman University, 02040, Adiyaman, Turkey.

Abstract

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.

Keywords


[1]S. Aytar Rough statistical Convergence, Numer. Funct. Anal. Optimi., 29(3),(2008), 291-303.
[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), 497-506.
[3]A. Esi , On some triple almost lacunary sequence spaces de ned by Orlicz functions, Research and Reviews:Discrete Mathematical Structures, 1(2), (2014), 16-25.
[4]A. Esi and M. Necdet Catalbas,Almost convergence of triple sequences, Global Journal of Mathematical Analysis,2(1), (2014), 6-10.
[5]A. Esi and E. Savas, On lacunary statistically convergent triple sequences in probabilistic normed
space,Appl.Math.and Inf.Sci., 9 (5) , (2015), 2529-2534.
[6]A. Esi, S. Araci and M. Acikgoz, Statistical Convergence of Bernstein Operators, Appl. Math. and Inf.Sci., 10 (6), (2016), 2083-2086.
[7]A. Esi, S. Araci and Ayten Esi, - Statistical Convergence of Bernstein polynomial sequences, Advances and Applications in Mathematical Sciences, 16 (3), (2017), 113-119.
[8]A. Esi, N. Subramanian and Ayten Esi, On triple sequence space of Bernstein operator of rough I convergence Pre-Cauchy sequences,Proyecciones Journal of Mathematics, 36 (4) , (2017), 567-587.
[9]A. Esi and N. Subramanian, Generalized rough Cesaro and lacunary statistical Triple di erence sequence spaces inprobability of fractional order defi ned by Musielak Orlicz function, International Journal of Analysis and
Applications, 16 (1) (2018), 16-24.
[10]A. Esi and N. Subramanian, On triple sequence spaces of Bernstein operator of X3 of rough λ-statistical convergence in probability of random variables defi ned by Musielak-Orlicz function, Int. J. open problems Compt.Math, 11 (2) (2019), 62-70.
[11]A. J. Dutta A. Esi and B.C. Tripathy,Statistically convergent triple sequence spaces de fined by Orlicz function, Journal of Mathematical Analysis, 4(2), (2013), 16-22.
[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), 71-79.
[13]H.Fast, Sur la convergence statistique, Colloq. Math. 2 (1951) 241-244.
[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), 633-640.
[16]H.X. Phu Rough convergence in normed linear spaces, Numer. Funct. Anal. Optimi., 22,(2001), 201-224.
[17]A. Sahiner, M. Gurdal and F.K. Duden, Triple sequences and their statistical convergence, Selcuk J. Appl. Math., 8 No. (2)(2007), 49-55.
[18]A. Sahiner, B.C. Tripathy , Some I related properties of triple sequences, Selcuk J. Appl. Math., 9 No. (2)(2008),9-18.
[19]N. Subramanian and A. Esi, The generalized tripled difference of X3 sequence spaces, Global Journal of Mathematical Analysis, 3 (2) (2015), 54-60.
[20]N. Subramanian and A. Esi, On triple sequence space of Bernstein operator of Χ 3 of rough λ-statistical convergence in probability de finited by Musielak-Orlicz function p-metric, Electronic Journal of Mathematical Analysis and Applications, 6 (1) (2018), 198-203.
[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), 72-78.
[23]S. Velmurugan and N. Subramanian, Bernstein operator of rough λ-statistically and ρ-Cauchy sequences convergence
on triple sequence spaces, Journal of Indian Mathematical Society, 85 (1-2) (2018), 257-265.
[24]H.Steinhaus Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951) 73-74.