Affiliations: [a] Department of Mathematics, Gazi University, Ankara, Turkey
| [b] Department of Mathematics, Aligarh Muslim University, India
| [c] Department of Mathematics, King Abdulaziz University, Saudi Arabia
Correspondence:
[*]
Corresponding author. Uğur Kadak, Department of Mathematics, Gazi University, TR-06500 Ankara, Turkey. E-mail: ugurkadak@gmail.com.
Abstract: This paper is devoted to studying weighted A-statistical convergence and statistical weighted A-summability of fuzzy sequences and their representations of sequences of λ-levels, which are intervals. We obtain necessary and sufficient conditions for the matrix A to be weighted fuzzy regular and derive some inclusion relations concerning these newly proposed methods. Furthermore we prove a fuzzy Korovkin type approximation theorem using statistically weighted A-summability and estimate the rates of weighted A-statistical convergence by means of the fuzzy modulus of continuity. Finally, based on a fuzzy analogue of Meyer-König and Zeller operators, we present an illustrative example to show that our proposed methods are stronger than the existing literature related to fuzzy Korovkin type approximation theorem.
Keywords: Weighted fuzzy regular matrix, weighted A-statistical convergence of fuzzy mappings, statistical weighted A-summability of fuzzy mappings, Korovkin type approximation theorems, rate of convergence
