Stancu type operators including generalized Brenke polynomials

TL;DR

This paper introduces Stancu type operators with generalized Brenke polynomials, analyzing their approximation properties for continuous functions and applying results to specific polynomial families.

Contribution

It presents a new class of Stancu type operators incorporating generalized Brenke polynomials and investigates their uniform approximation capabilities.

Findings

Established uniform approximation of continuous functions on closed intervals.

Derived convergence order estimates for the operators.

Applied results to Miller-Lee and Gould-Hopper polynomials.

Abstract

Our objective in this paper is to present the sequence of Stancu type operators including generalized Brenke polynomials. We answer the problem of uniform approximation of continuous functions on closed bounded interval and the problem of the order of this convergence estimate by known tools in approximation theory. Furthermore, we apply some of the results obtained in this work to Miller-Lee polynomials and Gould-Hopper polynomials.