Statistical equi-equal convergence of positive linear operators

Positivity - Many researchers have been interested in the concept of statistical convergence because of the fact that it is stronger than the classical convergence. Also, the concepts of...     

Korovkin type approximation theorem via Ka−convergence on weighted spaces

In this paper, we study the Korovkin type approximation theorem for K_a‐ convergence, which is an interesting convergence method on weighted spaces. We also study the rate of K_a?convergence by using the weighted modulus of continuity and afterwards, we present a nontrivial application.     

Relative uniform convergence of a sequence of functions at a point and Korovkin-type approximation theorems

Positivity - We prove a Korovkin-type approximation theorem using the relative uniform convergence of a sequence of functions at a point, which is a method stronger than the classical ones. We give...     

Approximation in statistical sense to <Emphasis Type="Italic">n</Emphasis>-variate B-continuous functions by positive linear operators

Our primary interest in the present paper is to prove a Korovkintype approximation theorem for sequences of positive linear operators defined on the space of all real valued n-variate B-continuous functions on a compact subset of the real n-dimensional space via statistical convergence. Also, we display an example such that our method of convergence is stronger than the usual convergence.     

A Korovkin-type theorem for double sequences of positive linear operators via power series method

In this paper, using power series method we obtain a Korovkin type theorem for double sequences of real valued functions defined on a compact subset of \(\mathbb {R}^{2}\)(the real two-dimensional space). We also present an example that satisfies our theorem. Finally, we calculate the rate of convergence.     

Statistical approximation to Bögel-type continuous and periodic functions

In this paper, considering A-statistical convergence instead of Pringsheim’s sense for double sequences, we prove a Korovkin-type approximation theorem for sequences of positive linear operators defined on the space of all real valued Bögel-type continuous and periodic functions on the whole real two-dimensional space. A strong application is also presented. Furthermore, we obtain some rates of A-statistical convergence in our approximation.