Approximation properties of a new family of Gamma operators and their applications

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

Korovkin type approximation via statistical e-convergence on two dimensional weighted spaces

In the present work, we prove a Korovkin theorem for statistical e-convergence on two dimensional weighted spaces. We show that our theorem is a non-trivial extension of some well-known Korovkin type approximation theorems. We also study the rate of statistical e-convergence by using the weighted modulus of continuity and afterwards we present an application in support of our result.

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

In this paper, we introduce an interesting kind of convergence for a double sequence called the uniform convergence at a point. We give an example and demonstrate a Korovkin-type approximation theorem for a double sequence of functions using the uniform convergence at a point. Then we show that our result is stronger than the Korovkin theorem given by Volkov and present several graphs. Finally, in the last section, we compute the rate of convergence.

Ideal relatively uniform convergence with Korovkin and Voronovskaya types approximation theorems

We introduce the notion of ideally relative uniform convergence of sequences of real valued functions. We then apply this notion to prove Korovkin-type approximation theorem, and then construct an illustrative example by taking (p,q)-Bernstein operators which proves that our Korovkin theorem is stronger than its classical version as well as statistical relative uniform convergence. The rate of ideal relatively uniform convergence of positive linear operators by means of modulus of continuity is calculated. Finally, the Voronovskaya-type approximation theorem is also investigated.

Dunkl analogue of Szász-mirakjan operators of blending type

In the present work, we construct a Dunkl generalization of the modified Szász-Mirakjan operators of integral form defined by Pǎltanea [1]. We study the approximation properties of these operators including weighted Korovkin theorem, the rate of convergence in terms of the modulus of continuity, second order modulus of continuity via Steklov-mean, the degree of approximation for Lipschitz class of functions and the weighted space. Furthermore, we obtain the rate of convergence of the considered operators with the aid of the unified Ditzian-Totik modulus of smoothness and for functions having derivatives of bounded variation.

Approximation by bivariate (p,q)-Baskakov–Kantorovich operators

The present paper deals with the bivariate{(p,q)}-Baskakov–Kantorovich operators and their approximation properties. First we construct the operators and obtain some auxiliary results such as calculations of moments and central moments, etc. Our main results consist of uniform convergence of the operators via the Korovkin theorem and rate of convergence in terms of modulus of continuity.

Korovkin Approximation Theorem with Ω Striped

In this paper, we discuss some theorem reached M. Mursaleen, there are several properties of statistical lacunary summability presented (Mursaleen, M. & Alotaibi,A., 2011; Mursaleen, M. &Alotaibi, A., 2011; Edely, O. H. & Mursaleen, M., 2009). This is concerned the motivate to narrowly delineated context denoted by Ω striped usage in prove our theorem (theorem A). We introduce some piecewise polynomial functions (Kopotun,K. A., 2006) and some results Korovkin theorem.

An asymptotic formula for a class of approximation processes of King’s type

In this paper we present a general class of linear positive operators of discrete type reproducing the third test function of Korovkin theorem. In a certain weighted space it forms an approximation process. A Voronovskaja-type result is established and particular cases are analyzed.