Bivaraiate Generalized Baskakov Kantorovich Operators

TL;DR

This paper extends generalized Baskakov Kantorovich operators to the bivariate case, analyzing their approximation properties, convergence rates, and derivative behaviors in weighted polynomial spaces.

Contribution

It introduces the bivariate extension of these operators and investigates their approximation capabilities and convergence properties.

Findings

Established degree of approximation for bivariate operators

Proved Voronovskaja type theorems for the operators

Analyzed the first order derivatives in weighted spaces

Abstract

This paper is in continuation of our work in \cite{PNM}, wherein we introduced generalized Baskakov Kantorovich operators $K_n^a(f;x)$ and established some approximation properties e.g. local approximation, weighted approximation, simultaneous approximation and $A-$statistical convergence. Also, we discussed the rate of convergence for functions having a derivative coinciding a.e. with a function of bounded variation. The purpose of this paper is to study the bivariate extension of the operators $K_n^a(f;x)$ and discuss results on the degree of approximation, Voronovskaja type theorems and their first order derivatives in polynomial weighted spaces.