Bernstein Operator of Rough λ-statistically and Ï Cauchy Sequences Convergence on Triple Sequence Spaces
Authors
-
Department of Mathematics, Hindustan Institute of Technology and Science, Chennai - 603 103 ,IN
S. Velmurugan -
Department of Mathematics, SASTRA University, Thanjavur-613 401 ,INN. Subramanian
DOI:
https://doi.org/10.18311/jims/2018/15896Keywords:
Bernstein Polynomial, Rough Statistical Convergence, Natural Density, Triple Sequences, rλ−Statistical Convergence, Ï−Cacuhy.Abstract
In this article, using the concept of natural density, we introduce the notion of Bernstein polynomials of rough λ−statistically and Ï−Cauchy triple sequence spaces. We deï¬ne the set of Bernstein polynomials of rough statistical limit points of a triple sequence spaces and obtain to λ−statistical convergence criteria associated with this set. We examine the relation between the set of Bernstein polynomials of rough λ−statistically and Ï− Cauchy triple sequences.
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Copyright (c) 2018 S. Velmurugan, N. Subramanian
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2017-07-27
Published 2018-01-04
References
S. Aytar, Rough statistical Convergence, Numerical Functional Analysis Optimization, 29(3), (2008), 291-303.
A. Esi , On some triple almost lacunary sequence spaces deï¬ned by Orlicz functions, Research and Reviews:Discrete Mathematical Structures, 1(2), (2014), 16-25.
A. Esi and M. Necdet Catalbas,Almost convergence of triple sequences, Global Journal of Mathematical Analysis, 2(1), (2014), 6-10.
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.
A. Esi, S. Araci and M. Acikgoz, Statistical Convergence of Bernstein Opera-tors,Appl.Math.and Inf.Sci., 10 (6) , (2016), 2083-2086.
A. J. Datta A. Esi and B.C. Tripathy,Statistically convergent triple sequence spaces deï¬ned by Orlicz function , Journal of Mathematical Analysis, 4(2), (2013), 16-22.
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.
S.K. Pal, D. Chandra and S. Dutta 2013. Rough ideal Convergence, Hacee. Jounral Mathematics and Statistics, 42(6), 633-640.
H.X. Phu 2001. Rough convergence in normed linear spaces, Numerical Functional Analysis Optimization, 22, 201-224.
A. Sahiner, M. Gurdal and F.K. Duden, Triple sequences and their statistical convergence, Selcuk J. Appl. Math. , 8 No. (2)(2007), 49-55.
A. Sahiner, B.C. Tripathy , Some I related properties of triple sequences, Selcuk J. Appl. Math., 9 No. (2)(2008,) 9-18.
N. Subramanian and A. Esi, The generalized tripled difference of χ3 sequence spaces, Global Journal of Mathematical Analysis, 3 (2) (2015), 54-60.
B.C. Tripathy and R. Goswami, On triple dierence sequences of real numbers in probabilistic normed spaces, Proyecciones Jour. Math., 33 (2) (2014), 157-174.
B.C. Tripathy and R. Goswami, Vector valued multiple sequences dened by Orlicz functions, Boletim da Sociedade Paranaense de Matemtica, 33 (1) (2015), 67-79.
B.C. Tripathy and R. Goswami, Multiple sequences in probabilistic normed spaces, Afrika Matematika, 26 (5-6) (2015), 753-760.
B.C. Tripathy and R. Goswami, Fuzzy real valued p-absolutely summable multiple sequences in probabilistic normed spaces, Afrika Matematika, 26 (7-8), 1281-1289.
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