# Generalized Kantorovich-Szász type operations involving Charlier polynomials

Volume 14, Issue 4, pp 222--249
Publication Date: January 05, 2021 Submission Date: July 25, 2020 Revision Date: November 29, 2020 Accteptance Date: December 02, 2020
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### Authors

P. N. Agrawal - Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India. Abhishek Kumar - Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India. Aditi Kar Gangopadhyay - Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India. Tarul Garg - Department of Applied Science, The NorthCap University, Gurugram-122017, India.

### Abstract

The purpose of this paper is to introduce a new kind of Kantorovich-Szász type operators based on Charlier polynomials and study its various approximation properties. We establish some local direct theorems, e.g., Voronovskaja type asymptotic theorem and an estimate of error by means of the Lipschitz type maximal function and the Peetre's K-functional. We also discuss the weighted approximation properties. Next, we construct a bivariate case of the above operators and study the degree of approximation with the aid of the complete and partial moduli of continuity. A Voronovskaja type asymptotic theorem and the order of convergence by considering the second order modulus of continuity are also proved. We define the associated Generalized Boolean Sum (GBS) operators and discuss the degree of approximation by using mixed modulus of smoothness for Bögel continuous and Bögel differentiable functions. Furthermore, by means of a numerical example it is shown that the proposed operators provide us a better approximation than the operators corresponding to the particular case $\wp=1$. We also illustrate the convergence of the bivariate operators and the associated GBS operators to a certain function and show that the GBS operators enable us a better error estimation than the bivariate operators using Matlab algorithm.

### Share and Cite

##### ISRP Style

P. N. Agrawal, Abhishek Kumar, Aditi Kar Gangopadhyay, Tarul Garg, Generalized Kantorovich-Szász type operations involving Charlier polynomials, Journal of Nonlinear Sciences and Applications, 14 (2021), no. 4, 222--249

##### AMA Style

Agrawal P. N., Kumar Abhishek, Gangopadhyay Aditi Kar, Garg Tarul, Generalized Kantorovich-Szász type operations involving Charlier polynomials. J. Nonlinear Sci. Appl. (2021); 14(4):222--249

##### Chicago/Turabian Style

Agrawal, P. N., Kumar, Abhishek, Gangopadhyay, Aditi Kar, Garg, Tarul. "Generalized Kantorovich-Szász type operations involving Charlier polynomials." Journal of Nonlinear Sciences and Applications, 14, no. 4 (2021): 222--249

### Keywords

• Voronovskaya theorem
• moduli of continuity
• Peetre's K-functional
• Bögel continuous function
• Bögel differentiable function

•  47A58