A Generalization of Post-Widder Operators Based on q-Integers

Abstract

In this paper we introduce a q-generalization of Post-Widder operators Pn,q. We give a Voronovskaja-type approximation result and rate of that convergence. We also study approximation properties of Pn,q in a weighted space. We also show that the rates of convergence of these generalized operators to approximating function f as weight are at least so faster than that of the classical Post-Widder operators.

Some Results on Post-Widder Operators Preserving Test Function x^r

“…These operators preserve constant functions only. The q analogue of these operators was recently studied by Aydin et al [3]. Earlier Rathore and Singh [15] (also for related results see [9]) established an asymptotic formula, and deduced inverse and saturation theorems in simultaneous approximation.…”