The Journal of the Indian Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

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
     

   Subscribe/Renew Journal


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.
Subscription Login to verify subscription
User
Notifications
Font Size


  • 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.


Abstract Views: 275

PDF Views: 0




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

Abstract Views: 275  |  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