Statistical fuzzy approximation by fuzzy positive linear operators

Authors:
George A. Anastassiou;Oktay Duman
Affiliations:
Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, USA;TOBB Economics and Technology University, Faculty of Arts and Sciences, Department of Mathematics, Söğütözü TR-06530, Ankara, Turkey
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

In this paper, we prove a Korovkin-type approximation theorem for fuzzy positive linear operators by using the notion of A-statistical convergence, where A is a non-negative regular summability matrix. This type of approximation enables us to obtain more powerful results than in the classical aspects of approximation theory settings. An application of this result is also given. Furthermore, we compute the rates of this statistical fuzzy convergence of the operators via the fuzzy modulus of continuity.