Approximation Properties of a Fractional Integral-Type Szász–Kantorovich–Stancu–Schurer Operator via Charlier Polynomials

Nadeem Rao, Mohammad Farid () and Nand Kishor Jha
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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
Nand Kishor Jha: Department of Mathematics, Chandigarh University, Mohali 140413, Punjab, India

Mathematics, 2025, vol. 13, issue 18, 1-17

Abstract: The goal of this manuscript is to introduce a new Stancu generalization of the modified Szász–Kantorovich operator connecting Riemann–Liouville fractional operators via Charlier polynomials. Further, some estimates are calculated as test functions and central moments. In the next section, we investigate some convergence analysis along with the rate of approximations. Moreover, we discuss the order of approximation of a higher-order modulus of smoothness with the help of some moments and establish some convergence results concerning Peetre’s K-functional, Lipschitz-type functions for a newly developed operator S K n + p , a v 1 , v 2 . We estimate some results related to Korovkin-, Voronovskaya-, and Grüss–Voronovskaya-type theorems.

Keywords: rate of convergence; order of approximation; mathematical operators; modulus of continuity; approximation algorithms; Peetre’s K-functional; Korovkin theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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