The Approximation Szász-Chlodowsky Type Operators Involving Gould-Hopper Type Polynomials

We introduce the Szász and Chlodowsky operators based on Gould-Hopper polynomials and study the statistical convergence of these operators in a weighted space of functions on a positive semiaxis. Further, a Voronovskaja type result is obtained for the operators containing Gould-Hopper polynomials. Finally, some graphical examples for the convergence of this type of operator are given

Fuzzy Korovkin type Theorems via deferred Cesaro and deferred Euler equi-statistical convergence

We establish a fuzzy Korovkin type approximation theorem by using $eq-stat^{D}_{CE}$(deferred Ces\'{a}ro and deferred Euler equi-statistical) convergence proposed by Saini et al. for continuous functions over $[a,b]$. Further, we determine the rate of convergence via fuzzy modulus of continuity

On the Approximation Properties of q−Analogue Bivariate λ-Bernstein Type Operators

In this article, we establish an extension of the bivariate generalization of the q-Bernstein type operators involving parameter λ and extension of GBS (Generalized Boolean Sum) operators of bivariate q-Bernstein type. For the first operators, we state the Volkov-type theorem and we obtain a Voronovskaja type and investigate the degree of approximation by means of the Lipschitz type space. For the GBS type operators, we establish their degree of approximation in terms of the mixed modulus of smoothness. The comparison of convergence of the bivariate q-Bernstein type operators based on parameters and its GBS type operators is shown by illustrative graphics using MATLAB software

Blending type approximation by bivariate generalized Bernstein type operators

In this article we establish an extension of the bivariate generalization of the Bernstein type operators involving parameters. For these operators we obtain a Voronovskaja type and Grüss Voronovskaja type theorems and the degree of approximation by means of the Lipschitz type space. Further, we present the associated Generalized Boolean Sum (GBS) operators and establish their degree of approximation in terms of the mixed modulus of smoothness. The comparison of convergence of the bivariate Bernstein type operators based on parameters and its GBS type operators is shown by illustrative graphics using MAPLE software. Mathematics Subject Classification (2010): 41A25, 26A15

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

The approximation of bivariate Chlodowsky-Szász-Kantorovich-Charlier-type operators

Abstract In this paper, we introduce a bivariate Kantorovich variant of combination of Szász and Chlodowsky operators based on Charlier polynomials. Then, we study local approximation properties for these operators. Also, we estimate the approximation order in terms of Peetre’s K-functional and partial moduli of continuity. Furthermore, we introduce the associated GBS-case (Generalized Boolean Sum) of these operators and study the degree of approximation by means of the Lipschitz class of Bögel continuous functions. Finally, we present some graphical examples to illustrate the rate of convergence of the operators under consideration