On statistical approximation properties of on statistical approximation properties of (p,q)-bleimann-butzer-hahn operators

TL;DR

This paper introduces a generalized class of (p,q)-Bleimann-Butzer-Hahn operators, establishes their statistical approximation properties, and analyzes their convergence rates, including bivariate extensions.

Contribution

It presents a new generalization of (p,q)-Bleimann-Butzer-Hahn operators and proves their statistical approximation properties with convergence rate analysis.

Findings

Established Korovkin's type statistical approximation theorem for the operators.

Derived the rate of convergence using the modulus of continuity.

Extended the operators to a bivariate setting.

Abstract

The aim of this paper is to introduce a generalization of the (p,q)-Bleimann-Butzer-Hahn operators based on (p,q)-integers and obtain Korovkin's type statistical approximation theorem for these operators. Also, we establish the rate of convergence of these operators using the modulus of continuity. Furthermore, we introduce (p,q)-Bleimann-Butzer-Hahn bivariate operators.