Approximation by generalized Szasz operators involving Sheffer polynomials (original) (raw)

Approximation by Szász Type Operators Including Sheffer Polynomials

Journal of Mathematics and Applications, 2017

In present article, we discuss voronowskaya type theorem, weighted approximation in terms of weighted modulus of continuity for Szász type operators using Sheffer polynomials. Lastly, we investigate statistical approximation for these sequences.

Approximation Properties of Generalized Szász-Type Operators

Acta Mathematica Vietnamica, 2018

In the present paper, we study some approximation properties of the generalized Szász type operators introduced by V. Miheşan (Creat. Math. Inf. 17:466-472, 2008). We present a quantitative Voronovskaya-type theorem, local approximation theorem by means of second-order modulus of continuity and weighted approximation for these operators. The rate of convergence for differential functions whose derivatives are of bounded variation is also obtained.

Approximation by a generalized Szász type operator for functions of two variables

Miskolc Mathematical Notes, 2014

In the present paper, we define a new Szász-Mirakjan type operator in exponential weighted spaces for functions of two variables having exponential growth at infinity using a method given by Jakimovski-Leviatan. This operator is a generalization of two variables of an operator defined by A. Ciupa [1]. In this study, we investigate approximation properties and also estimate the rate of convergence for this new operator.

Approximation by a generalization of Szasz-Mirakjan type operators

Studia Universitatis Babes-Bolyai Matematica, 2020

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 Properties of Sz�asz Type Operators Based on Charlier Polynomials

In the present paper, we study some approximation properties of the Sz�asz type operators involving Charlier polynomials introduced by S. Varma and F. Ta�sdelen (Math. Comput. Modelling, 56 (5-6) (2012) 108-112). First, we establish approximation in a Lipschitz type space and weighted approximation theorems for these operators. Then, we obtain the error in the approximation of functions having derivatives of bounded variation.

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

Journal of inequalities and applications, 2017

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.

Approximation by modified Kantorovich–Szász type operators involving Charlier polynomials

Advances in Difference Equations, 2020

In this paper, we give some direct approximation results by modified Kantorovich-Szász type operators involving Charlier polynomials. Further, approximation results are also developed in polynomial weighted spaces. Moreover, for the functions of bounded variation, approximation results are proved. Finally, some graphical examples are provided to show comparisons of convergence between old and modified operators towards a function under different parameters and conditions.

Rate of convergence by Kantorovich-Szász type operators based on Brenke type polynomials

Journal of Inequalities and Applications

The present paper deals with the approximation properties of the univariate operators which are the generalization of the Kantorovich-Szász type operators involving Brenke type polynomials. We investigate the order of convergence by using Peetre's K-functional and the Ditzian-Totik modulus of smoothness and study the degree of approximation of the univariate operators for continuous functions in a Lipschitz space, a Lipschitz type maximal function and a weighted space. The rate of approximation of functions having derivatives equivalent with a function of bounded variation is also obtained.

Approximation Properties of Extended Beta-Type Szász–Mirakjan Operators

Iranian Journal of Science

In this article, we introduce generalized beta extension of Sz$$\acute{a}$$ a ´ sz-integral type operators and study their approximation properties. First, we calculate the some estimates for these operators. Further, we study the uniform convergence and order of approximation in terms of Korovkin-type theorem and modulus of continuity for the space of univariate continuous functions and bivariate continuous functions in their sections.. Moreover, numerical estimates and graphical representations for convergence of one- and two-dimensional sequences of operators are studied. In continuation, local and global approximation properties are studied in terms of the first- and second-order modulus of smoothness, Peetre’s K-functional and weight functions in various functional spaces.