On some summability methods for a q-analogue of an integral type operator based on multivariate q-Lagrange polynomials

TL;DR

This paper introduces a q-analogue of a multivariate integral operator based on q-Lagrange polynomials, exploring its approximation properties using Korovkin-type theorems under advanced convergence methods.

Contribution

It develops a new q-analogue operator involving multivariate q-Lagrange polynomials and establishes convergence theorems in novel settings.

Findings

Established Korovkin-type approximation theorems for the q-analogue operator.

Proved convergence under deferred weighted A-statistical and power series methods.

Extended classical approximation results to a multivariate q-analogue context.

Abstract

The present paper considers a q-analogue of an operator defined by Erku\c{s}-Duman et al. (Calcolo, 45(1) (2008), 53-67) involving q-Lagrange polynomials in several variables. The Korovkin type theorems in the settings of deferred weighted A-statistical convergence and the power series method are investigated.