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.

Approximation by Bézier Variant of Baskakov-Durrmeyer-Type Hybrid Operators

We give a Bézier variant of Baskakov-Durrmeyer-type hybrid operators in the present article. First, we obtain the rate of convergence by using Ditzian-Totik modulus of smoothness and also for a class of Lipschitz function. Then, weighted modulus of continuity is investigated too. We study the rate of point-wise convergence for the functions having a derivative of bounded variation. Furthermore, we establish the quantitative Voronovskaja-type formula in terms of Ditzian-Totik modulus of smoothness at the end.

On approximation properties of a new construction of Baskakov operators

The purpose of this research is to construct sequences of Baskakov operators such that their construction consists of a function σ by use of two function sequences, $\xi _{n} $ ξ n and $\eta _{n} $ η n . In these operators, σ not only features the sequences of operators but also features the Korovkin function set $\lbrace 1,\sigma ,\sigma ^{2} \rbrace $ { 1 , σ , σ 2 } in a weighted function space such that the operators fix exactly two functions from the set. Thereafter, weighted uniform approximation on an unbounded interval, the degree of approximation with regards to a weighted modulus of continuity, and an asymptotic formula of the new operators are presented. Finally, some illustrative results are provided in order to observe the approximation properties of the newly defined Baskakov operators. The results demonstrate that the introduced operators provide better results in terms of the rate of convergence according to the selection of σ.

GENUINE MODIFIED BASKAKOV-DURRMEYER OPERATORS

The present paper deals with genuine Baskakov Durrmeyer operators which have preserved certain functions. We have obtained quantitative Voronovskaya and quantitative Grüss type Voronovskaya theorems using the weighted modulus of continuity. These results include the preservation properties of the classical genuine Baskakov Durrmeyer operators.

Quantitative estimates for Szász operators and its hybrid variant

The present article deals with the study on approximation properties of well known Sz?sz-Mirakyan operators. We estimate the quantitative Voronovskaja type asymptotic formula for the Sz?sz-Baskakov operators and difference between Sz?sz-Mirakyan operators and the hybrid Sz?sz operators having weights of Baskakov basis in terms of the weighted modulus of continuity

Approximation by a generalization of Szasz-Mirakjan type operators

In the present paper we propose a new generalization of Sz\'{a}sz-Mirakjan-type operators. We discuss their weighted convergence and rate of convergence via weighted modulus of continuity. We also give an asymptotic estimate through Voronovskaja type result for these operators.

Approximation by Szász-Jakimovski-Leviatan-Type Operators via Aid of Appell Polynomials

The main purpose of the present article is to construct a newly Szász-Jakimovski-Leviatan-type positive linear operators in the Dunkl analogue by the aid of Appell polynomials. In order to investigate the approximation properties of these operators, first we estimate the moments and obtain the basic results. Further, we study the approximation by the use of modulus of continuity in the spaces of the Lipschitz functions, Peetres K-functional, and weighted modulus of continuity. Moreover, we study A-statistical convergence of operators and approximation properties of the bivariate case.

Modified Lupaş-Jain operators

The goal of this paper is to propose a modification of Lupaş-Jain operators based on a function ρ having some properties. Primarily, the convergence of given operators in weighted spaces is discussed. Then, order of approximation via weighted modulus of continuity is computed for these operators. Further, Voronovskaya type theorem in quantitative form is taken into consideration, as well. Ultimately, some graphical results that illustrate the convergence of investigated operators to f are given.

Approximation for difference of Lupaş and some classical operators

The approximation of difference of two linear positive operators having different basis functions is discussed in the present article. The quantitative estimates in terms of weighted modulus of continuity for the difference of Lupa? operators and the classical ones are obtained, viz. Lupa? and Baskakov operators, Lupa? and Sz?sz operators, Lupa? and Baskakov-Kantorovich operators, Lupa? and Sz?sz-Kantorovich operators.

The Approximation of Bivariate Blending Variant Szász Operators Based Brenke Type Polynomials

We have constructed a new sequence of positive linear operators with two variables by using Szasz-Kantorovich-Chlodowsky operators and Brenke polynomials. We give some inequalities for the operators by means of partial and full modulus of continuity and obtain a Lipschitz type theorem. Furthermore, we study the convergence of Szasz-Kantorovich-Chlodowsky-Brenke operators in weighted space of function with two variables and estimate the rate of approximation in terms of the weighted modulus of continuity.