A Study of Szász–Durremeyer-Type Operators Involving Adjoint Bernoulli Polynomials

Nadeem Rao, Mohammad Farid () and Rehan Ali
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Nadeem Rao: Department of Mathematics, University Center for Research and Development, Chandigarh University, Mohali 140413, Punjab, India
Mohammad Farid: Department of Mathematics, College of Science, Qassim University, Saudi Arabia
Rehan Ali: Department of Mathematics, Central University of Kashmir, Jammu and Kashmir 191131, India

Mathematics, 2024, vol. 12, issue 23, 1-15

Abstract: This research work introduces a connection of adjoint Bernoulli’s polynomials and a gamma function as a sequence of linear positive operators. Further, the convergence properties of these sequences of operators are investigated in various functional spaces with the aid of the Korovkin theorem, Voronovskaja-type theorem, first order of modulus of continuity, second order of modulus of continuity, Peetre’s K-functional, Lipschitz condition, etc. In the last section, we extend our research to a bivariate case of these sequences of operators, and their uniform rate of approximation and order of approximation are investigated in different functional spaces. Moreover, we construct a numerical example to demonstrate the applicability of our results.

Keywords: Bernoulli polynomials; mathematical operators; gamma function; rate of convergence; Voronovskaja theorem; modulus of smoothness; approximation algorithms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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