q-Gamma Type Operators for Approximating Functions of a Polynomial Growth

Abstract

We investigate the rate of convergence of the operators introduced by Singh et al. (Linear Multilinear Algebra, 2022. https://doi.org/10.1080/03081087.2021.1960260) for functions of a polynomial growth. By using Steklov means, we obtain an estimate of error for these operators in terms of the modulus of continuity of order two. We derive an asymptotic theorem of Voronovskaja type and its quantitative form. Further, we modify these operators to examine the approximation of smooth functions in the above polynomial weighted space, i.e. a space of functions under a norm that involves multiplication by a polynomial function referred to as the weight and show that we achieve better approximation. We also discuss the convergence in the Lipschitz space and a Voronovskaja type asymptotic result.