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

### 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.### 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.

*Proyecciones (Antofagasta, On line)*, vol. 38, no. 4, pp. 783-798, Oct. 2019.

Copyright (c) 2019 M. Jeyaram Bharathi, S. Velmurugan, Ayhan Esi, N. Subramanian

This work is licensed under a Creative Commons Attribution 4.0 International License.