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 aforesaidnotions. 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.
Highlights
Introduction and PreliminariesMoore [31] was the first who presented the notion of of uniform convergence of sequence of functions associated with a scale function, and later Chittenden [12] studied this concept
The main objective of the proposed work is to establish a fuzzy approximation (Korovkin-type) theorem by using relatively deferred Norlund equi-statistical convergence based on ∆αh,β,γ and further to estimate its statistical fuzzy rates with the help of the fuzzy modulus of continuity
We intend to investigate here the fuzzy rate of the relatively equi-statistical convergence of a sequence of fuzzy positive linear operators defined from CF (E) into itself based on the fuzzy modulus of continuity
Summary
Moore [31] was the first who presented the notion of of uniform convergence of sequence of functions associated with a scale function, and later Chittenden [12] studied this concept. The use of statistical convergence in approximation theory has enabled the researchers to achieve more powerful outcomes than that of the classical aspects of convergence In this context, we refer to the recent works [9], [10], [15], [14], [13], [20], [21], [24], [22], [23], [25], [33], [34], [35], [36], [37], [38] and [40]. The main objective of the proposed work is to establish a fuzzy approximation (Korovkin-type) theorem by using relatively deferred Norlund equi-statistical convergence based on ∆αh,β,γ and further to estimate its statistical fuzzy rates with the help of the fuzzy modulus of continuity
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