A Certain Class of Relatively Equi-Statistical Fuzzy Approximation Theorems

Authors

  • Susanta Kumar Paikray
  • Priyadarsini Parida
  • S. A. Mohiuddine

DOI:

https://doi.org/10.29020/nybg.ejpam.v13i5.3711

Keywords:

Deferred Nörlund mean, Relatively statistical uniform convergence, Relatively equi-statistical convergence, Fuzzy positive linear operator, Fuzzy Korovkin-type theo- rem, Fuzzy rate of relatively equi-statistical convergence

Abstract

The aim of this paper is to introduce the notions of relatively deferred Norlund uniform statistical convergence as well as relatively deferred Norlund point-wise statistical convergence through the dierence operator of fractional order of fuzzy-number-valued sequence of functions, and a type of convergence which lies between aforesaid notions, namely, relatively deferred Norlund equi-statistical convergence. Also, we investigate the inclusion relations among these aforesaid
notions. As an application point of view, we establish a fuzzy approximation (Korovkin-type) theorem by using our new notion of relatively deferred Norlund equi-statistical convergence and intimate that this result is a non-trivial generalization of several well-established fuzzy Korovkin-type theorems which were presented in earlier works. Moreover, we estimate the fuzzy rate of the relatively deferred Norlund equi-statistical convergence involving a non-zero scale function by using the fuzzy modulus of continuity.

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Published

2020-12-27

Issue

Section

Special Issue Dedicated to Professor Hari M. Srivastava on the Occasion of his 80th Birthday

How to Cite

A Certain Class of Relatively Equi-Statistical Fuzzy Approximation Theorems. (2020). European Journal of Pure and Applied Mathematics, 13(5), 1212-1230. https://doi.org/10.29020/nybg.ejpam.v13i5.3711

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