On rough convergence of triple sequence spaces of Bernstein-Stancu operators of fuzzy numbers defined by a metric function

Authors

  • M. Bharathi Hindustan Institute of Technology and Science.
  • S. Velmurugan Hindustan Institute of Technology and Science.
  • Ayhan Esi Adiyaman University. https://orcid.org/0000-0003-3137-3865
  • N. Subramanian SASTRA University.

DOI:

https://doi.org/10.22199/issn.0717-6279-2019-04-0051

Keywords:

Triple sequences, Rough convergence, Closed and convex, Cluster points and rough limit points, Fuzzy numbers, Bernstein-Stancu polynomials

Abstract

We define the concept of rough limit set of a triple sequence space of Bernstein-Stancu polynomials of fuzzy numbers and obtain the relation between the set of rough limit and the extreme limit points of a triple sequence space of Bernstein-Stancu polynomials of fuzzy numbers. Finally, we investigate some properties of the rough limit set of Bernstein-Stancu polynomials.

Author Biographies

M. Bharathi, Hindustan Institute of Technology and Science.

Dept. of Mathematics.

S. Velmurugan, Hindustan Institute of Technology and Science.

Dept. of Mathematics.

Ayhan Esi, Adiyaman University.

Dept. of Mathematics.

N. Subramanian, SASTRA University.

Dept. of Mathematics

References

S. Aytar, “Rough statistical convergence”, Numerical functional analysis and optimization, vol. 29, no. 3-4, pp. 291-303, May 2008, doi: 10.1080/01630560802001064.

S. Aytar, “The rough limit set and the core of a real sequence”, Numerical functional analysis and optimization, vol. 29, no. 3-4, pp. 283-290, May 2008, doi: 10.1080/01630560802001056.

A. Esi, “On some triple almost lacunary sequence spaces defined by Orlicz functions”, Research and reviews: discrete mathematical structures, vol. 1, no. 2, pp. 16-25, 2014. [On line]. Available: https://bit.ly/2Mym1pj

A. Esi and M. Catalbas, “Almost convergence of triple sequences”, Global journal of mathematical analysis, vol. 2, no. 1, pp. 6-10, 201, doi: 10.14419/gjma.v2i1.1709.

A. Esi and E. Savas, “On lacunary statistically convergent triple sequences in probabilistic normed space”, Applied mathematics & information sciences, vol. 9, no. 5, pp. 2529-2534, Sep. 2015. [On line]. Available: https://bit.ly/2pGbPll

A. Esi, S. Araci and M. Acikgoz, “Statistical convergence of Bernstein operators”, Applied mathematics & information sciences, vol. 10, no. 6, pp. 2083-2086, Nov. 2016, doi: 10.18576/amis/100610.

A. Esi, S. Araci and A. Esi, “λ-statistical convergence of Bernstein polynomial sequences”, Advances and applications in mathematical sciences, vol. 16, no. 3, pp. 113-119, 2017.

A. Esi, N. Subramanian and A. Esi, “On triple sequence space of Bernstein operator of rough I− convergence pre-cauchy sequences”, Proyecciones (Antofagasta, En línea), vol. 36, no. 4, pp. 567-587, Dec. 2017, doi: 10.4067/S0716-09172017000400567.

A. J. Dutta A. Esi and B. Tripathy, “Statistically convergent triple sequence spaces defined by Orlicz function”, Journal of mathematical analysis, vol. 4, no. 2, pp. 16-22, 2013. [On line]. Available: https://bit.ly/2VX5XAl

S. Debnath, B. Sarma and B. Das, “Some generalized triple sequence spaces of real numbers”, Journal of nonlinear analysis and optimization, vol. 6, no. 1, pp. 71-79, May 2015. [On line]. Available: https://bit.ly/2oMTmDW

E. Dündar, C. Cakan, “Rough I− convergence”, Accepted on Demonstratio mathematica.

H. Phu, “Rough convergence in normed linear spaces”, Numerical functional analysis and optimization, vol. 22, no. 1-2, pp. 199-222, 2001, doi: 10.1081/NFA-100103794.

H. Phu, “Rough continuity of linear operators”, Numerical functional analysis and optimization, vol. 23, no. 1-2, pp. 139-146, 2002, doi: 10.1081/NFA-120003675.

H. Phu, “Rough convergence in infinite dimensional normed spaces”, Numerical functional analysis and optimization, vol. 24, no. 3-4, pp. 285-301, 2003, doi: 10.1081/NFA-120022923.

A. Sahiner, M. Gurdal and F. Duden, “Triple sequences and their statistical convergence”, Selcuk journal of applied mathematics. vol. 8, no. 2, pp. 49-55, 2007. [On line]. Available: https://bit.ly/33M5jbD

A. Sahiner, B. Tripathy, “Some I related properties of triple sequences”, Selcuk journal of applied mathematics, vol. 9, no. 2, pp. 9-18, 2008. [On line]. Available: https://bit.ly/2BuPSIA

N. Subramanian and A. Esi, “The generalized tripled difference of χ3 sequence spaces”, Global journal of mathematical analysis, vol. 3, no. 2, pp. 54-60, 2015, doi: 10.14419/gjma.v3i2.4412.

Published

2019-10-22

How to Cite

[1]
M. J. Bharathi, S. Velmurugan, A. Esi, and N. Subramanian, “On rough convergence of triple sequence spaces of Bernstein-Stancu operators of fuzzy numbers defined by a metric function”, Proyecciones (Antofagasta, On line), vol. 38, no. 4, pp. 783-798, Oct. 2019.

Issue

Section

Artículos

Most read articles by the same author(s)