Generalized Bernstein-Chlodowsky-Kantorovich type operators involving Gould-Hopper polynomials

Volume 14, Issue 5, pp 324--338 http://dx.doi.org/10.22436/jnsa.014.05.03
Publication Date: February 14, 2021 Submission Date: November 16, 2020 Revision Date: December 30, 2020 Accteptance Date: January 15, 2021

Authors

P. N. Agrawal - Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India. Sompal Singh - Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India.


Abstract

In the present article, we establish a link between the theory of positive linear operators and the orthogonal polynomials by defining Bernstein-Chlodowsky-Kantorovich operators based on Gould-Hopper polynomials (orthogonal polynomials) and investigate the degree of convergence of these operators for unbounded continuous functions having a polynomial growth. In this connection, the moments of the operators are derived first, and then the approximation degree of the considered operators is established by means of the complete and the partial moduli of continuity. Next, we focus on the rate of convergence of these operators for functions in a weighted space. The associated Generalized Boolean Sum (GBS) operator of the operators under study is defined, and the degree of approximation is studied with the aid of the mixed modulus of smoothness and the Lipschitz class of Bögel continuous functions.


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ISRP Style

P. N. Agrawal, Sompal Singh, Generalized Bernstein-Chlodowsky-Kantorovich type operators involving Gould-Hopper polynomials, Journal of Nonlinear Sciences and Applications, 14 (2021), no. 5, 324--338

AMA Style

Agrawal P. N., Singh Sompal, Generalized Bernstein-Chlodowsky-Kantorovich type operators involving Gould-Hopper polynomials. J. Nonlinear Sci. Appl. (2021); 14(5):324--338

Chicago/Turabian Style

Agrawal, P. N., Singh, Sompal. "Generalized Bernstein-Chlodowsky-Kantorovich type operators involving Gould-Hopper polynomials." Journal of Nonlinear Sciences and Applications, 14, no. 5 (2021): 324--338


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