Approximation by (p,q)-Lorentz polynomials on a compact disk

TL;DR

This paper introduces (p,q)-Lorentz polynomials, a new approximation tool based on (p,q)-integers, providing quantitative estimates and exact orders of approximation for analytic functions on compact disks.

Contribution

It presents the first development of (p,q)-Lorentz polynomials and establishes their approximation properties with precise quantitative estimates.

Findings

Derived Voronovskaja-type theorems for (p,q)-Lorentz polynomials.

Established exact orders of simultaneous approximation.

Extended approximation theory to complex analytic functions on compact disks.

Abstract

In this paper, we introduce a new analogue of Lorentz polynomials based on (p,q)-integers and we call it as (p,q)-Lorentz polynomials. We obtain quantitative estimate in the Voronovskaja's type thoerem and exact orders in simultaneous approximation by the complex (p,q)-Lorentz polynomials of degree n, where q > p > 1 attached to analytic functions in compact disks of the complex plane.