A Certain Class of Relatively Equi-Statistical Fuzzy Approximation Theorems

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

Abstract

The aim of this paper is to introduce the notions of relatively deferred Nörlund 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 Nörlund 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 Nörlund equi-statistical convergence involving a non-zero scale function by using the fuzzy modulus of continuity.

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

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