Sevda Karakuş

Statistical Convergence of Double Sequences on Probabilistic Normed Spaces

The concept of statistical convergence was presented by Steinhaus in 1951. This concept was extended to the double sequences by Mursaleen and Edely in 2003. Karakus has recently introduced the concept of statistical convergence of ordinary (single) sequence on probabilistic normed spaces. In this paper, we define statistical analogues of convergence and Cauchy for double sequences on probabilistic normed spaces. Then we display an exampl e such that our method of convergence is stronger than usual convergence on probabilistic normed spaces. Also we give a useful characterization for statistically convergent double sequences.

Statistical A-summability of positive linear operators

In this paper, using the concept of statistical A-summability which is stronger than the A-statistical convergence we provide a Korovkin-type approximation theorem. We also compute the rates of statistical A-summability of a sequence of positive linear operators.

Statistical σ approximation to max-product operators

In this paper, using the concept of statistical @s-convergence which is stronger than statistical convergence, we obtain a statistical @s approximation theorem for a general sequence of max-product operators, including Shepard type operators, although its classical limit fails. We also compute the corresponding statistical @s rates of the approximation.

A-SUMMATION PROCESS AND KOROVKIN-TYPE APPROXIMATION THEOREM FOR DOUBLE SEQUENCES OF POSITIVE LINEAR OPERATORS

The aim of this paper is to present a Korovkin-type approximation theorem on the space of all continuous real valued functions on any compact subset of the real two-dimensional space by using a A-summation process. We also study the rates of convergence of positive linear operators with the help of the modulus of continuity.

Equi-statistical σ -convergence of positive linear operators

In this paper we introduce the notion of equi-statistical @s-convergence which is stronger than the uniform convergence (in the ordinary sense), statistical uniform convergence and statistical uniform @s-convergence. Then, we also give its use in the Korovkin-type approximation theory. We also compute the rate of equi-statistical @s-convergence of a sequence of positive linear operators.

Four-dimensional matrix transformation and A-statistical fuzzy Korovkin type approximation

Abstract In this paper, we prove a fuzzy Korovkin-type approximation theorem for fuzzy positive linear operators by using A-statistical convergence for four-dimensional summability matrices. Also, we obtain rates of A-statistical convergence of a double sequence of fuzzy positive linear operators for four-dimensional summability matrices.