Characterization of deferred type statistical convergence and P-summability method for operators: Applications to q-Lagrange-Hermite operator

TL;DR

This paper explores advanced convergence methods for positive linear operators, establishing new approximation results and applying them to a multivariate q-Lagrange-Hermite polynomial operator.

Contribution

It introduces new Korovkin-type theorems for deferred type statistical convergence and P-summability, and applies these to a novel multivariate q-Lagrange-Hermite operator.

Findings

Established Korovkin-type approximation theorems for the convergence techniques.

Proved the applicability of the theorems to a multivariate q-Lagrange-Hermite operator.

Demonstrated the effectiveness of the methods in operator approximation.

Abstract

The present work considers two important convergence techniques, namely deferred type statistical convergence and P-summability method in respect of positive linear operators. With regard to these techniques, we state and prove two general non-trivial Korovkin type approximation results for such operators. Further, we define an operator based on multivariate q-Lagrange-Hermite polynomials and exhibit the applicability of our general theorems.