A Korovkin type theorem is established in the space C̃b[0,∞) of all uniformly continuous and bounded functions on [0,∞) for a sequence of positive linear operators, the approximation error being estimated with the aid of the usual modulus of continuity. As applications we obtain quantitative results for q-Baskakov operators. Mathematics Subject Classification (2010): 41A36, 41A25.

In this present paper, we study an approximation properties of modified Baskakov-Gamma operator. Using Korovkin type theorem first give Secondly, compute the rate convergence operator by means modulus continuity and weighted spaces. Finally, Voronovskaya

This study introduces (p,q)-hybrid Durrmeyer-Stancu type linear positive operators, which are generalized forms of q-hybrid Durrmeyer-Stancu-type operators and examines their approximation properties. The first modulus continuity on a finite interval is introduced using Peetre’s K-functional. Then, the weighted theorem in space provided Gadzhiev’s Korovkin-type theorem. Finally, these operators...

In this paper, we introduce the notion of statistical (λ, μ)-summability and find its relation with (λ, μ)-statistical convergence. We apply this new method to prove a Korovkin type approximation theorem for functions of two variables. Furthermore, we provide an example in support to show that our result is stronger than the previous ones.

In this paper, we define and study q-statistical limit point, cluster q-statistically Cauchy, q-strongly Cesàro statistically C1q-summable sequences. We establish relationships of convergence with Further, apply to prove a Korovkin type approximation theorem.

The purpose of this paper is twofold. First, the definition of new statistical convergence with Fibonacci sequence is given and some fundamental properties of statistical convergence are examined. Second, we provide various approximation results concerning the classical Korovkin theorem via Fibonacci type statistical convergence.

In this paper we consider the notion of A2 -statistical convergence for real double sequences which is an extension of the notion of AI -statistical convergence for real single sequences introduced by Savas, Das and Dutta. We primarily apply this new notion to prove a Korovkin type approximation theorem. In the last section, we study the rate of A2 -statistical convergence.

Abstract The present paper introduces a new modification of Gamma operators that protects polynomials in the sense Bohman–Korovkin theorem. In order to examine their approximation behaviours, properties newly introduced such as Voronovskaya-type theorems, rate convergence, weighted approximation, and pointwise estimates are presented. Finally, we some numerical examples verify constructed an pr...