ABSTRACT KOROVKIN THEOREMS VIA RELATIVE MODULAR CONVERGENCE FOR DOUBLE SEQUENCES OF LINEAR OPERATORS

We will obtain an abstract version of the Korovkin type approximation theorems with respect to the concept of statistical relative convergence in modular spaces for double sequences of positive linear operators. We will give an application showing that our results are stronger than classical ones. We will also study an extension to non-positive operators

Summation process of Korovkin type approximation theorem

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Korovkin-Type Theorems for Modular --Statistical Convergence

We deal with a new type of statistical convergence for double sequences, calledΨ-A-statistical convergence, and we prove a Korovkin-type approximation theorem with respect to this type of convergence in modular spaces. Finally, we give some application to moment-type operators in Orlicz spaces

A THEORY OF VARIATIONS VIA P-STATISTICAL CONVERGENCE

We introduce some notions of variation using the statistical convergence with respect to power series method. By the use of the notions of variation, we prove criterions that can be used to verify convergence without using limit value. Also, some results that give relations between P-statistical variations are studiedPublishe

Korovkin-Type Theorems for Modular Ψ

We deal with a new type of statistical convergence for double sequences, called Ψ-A-statistical convergence, and we prove a Korovkin-type approximation theorem with respect to this type of convergence in modular spaces. Finally, we give some application to moment-type operators in Orlicz spaces

Equi-Statistical Extension of the Korovkin Type Approximation Theorem

In this paper using equi-statistical convergence, which is stronger than the usual uniform convergence and statistical uniform convergence, we obtain a general Korovkin type theorem. Then, we construct examples such that our new approximation result works but its classical and statistical cases do not work

Approximation for periodic functions via statistical A-summability

In this paper, using the concept of statistical A-summability which is stronger than the A-statistical convergence, we prove a Korovkin type approxima-tion theorem for sequences of positive linear operator de ned on C (R) which is the space of all 2 -periodic and continuous functions on R, the set of all real numbers. We also compute the rates of statistical A-summability of sequence of positive linear operators

Approximation in statistical sense by n−multiple sequences of fuzzy positive linear operators

Our primary interest in the present paper is to prove a Korovkin- type approximation theorem for n − multiple sequences of fuzzy positive linear operators via statistical convergence. Also, we display an example such that our method of convergence is stronger than the usual convergence

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

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