A Certain Class of Relatively Equi-Statistical Fuzzy Approximation Theorems
DOI:
https://doi.org/10.29020/nybg.ejpam.v13i5.3711Keywords:
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 convergenceAbstract
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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