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Bernstein Operator of Rough λ-Statistically and ρ Cauchy Sequences Convergence on Triple Sequence Spaces


Affiliations
1 Department of Mathematics, Hindustan Institute of Technology and Science, Chennai - 603 103, India
2 Department of Mathematics, SASTRA University, Thanjavur-613 401, India
     

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In this article, using the concept of natural density, we introduce the notion of Bernstein polynomials of rough λ−statistically and ρ−Cauchy triple sequence spaces. We define 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 ρ−Cauchy triple sequences.

 

 


Keywords

Bernstein Polynomial, Rough Statistical Convergence, Natural Density, Triple Sequences, rλ−Statistical Convergence, ρ−Cacuhy.
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  • S. Aytar, Rough statistical Convergence, Numerical Functional Analysis Optimization, 29(3), (2008), 291-303.

  • A. Esi , On some triple almost lacunary sequence spaces defined 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 defined 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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  • Bernstein Operator of Rough λ-Statistically and ρ Cauchy Sequences Convergence on Triple Sequence Spaces

Abstract Views: 343  |  PDF Views: 0

Authors

S. Velmurugan
Department of Mathematics, Hindustan Institute of Technology and Science, Chennai - 603 103, India
N. Subramanian
Department of Mathematics, SASTRA University, Thanjavur-613 401, India

Abstract


In this article, using the concept of natural density, we introduce the notion of Bernstein polynomials of rough λ−statistically and ρ−Cauchy triple sequence spaces. We define 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 ρ−Cauchy triple sequences.

 

 


Keywords


Bernstein Polynomial, Rough Statistical Convergence, Natural Density, Triple Sequences, rλ−Statistical Convergence, ρ−Cacuhy.

References