Statistical approximation properties of Stancu type $q$-Baskakov-Kantorovich operators

TL;DR

This paper introduces a generalized class of Baskakov-Kantorovich operators based on q-integers, analyzing their statistical approximation properties and convergence rates, including a bivariate extension.

Contribution

It presents a new Stancu type generalization of q-Baskakov-Kantorovich operators and studies their statistical approximation properties, including convergence rates and a bivariate version.

Findings

Operators exhibit statistical convergence with established rates.

The modulus of continuity and Lipschitz functions quantify approximation quality.

Bivariate operators also demonstrate statistical approximation properties.

Abstract

In the present paper, we consider Stancu type generalization of Baskakov-Kantorovich operators based on the q-integers and obtain statistical and weighted statistical approximation properties of these operators. Rates of statistical convergence by means of the modulus of continuity and the Lipschitz type function are also established for said operators. Finally, we construct a bivariate generalization of the operator and also obtain the statistical approximation properties.