Generalized Ismail-Durrmeyer type operators involving Sheffer polynomials

Abstract

In this paper, we introduce a new kind of Durrmeyer variant of generalized Ismail operators based on Sheffer polynomials. These type of polynomials are a generalization of Appell polynomials and a special case of Boas-Buck-type polynomials. We study the convergence of these operators with the help of universal Korovkin type theorem, modulus of continuity, Peetre's $ K $-functional and the class of Lipschitz type functions. Furthermore, We extend this study to include Voronovskaja-type asymptotic results, quantitative-Voronovskaja and Gr$ \ddot{u} $ss-Voronovskaja type theorems and the convergence rate of these operators for functions in a polynomial weighted space by means of the weighted modulus of continuity.