Some Approximation Properties by Sz\'asz-P{\u{a}}lt{\u{a}}nea type Operators involving the Appell Polynomials of class $A^2$

TL;DR

This paper introduces new Szász-Păltănea type operators involving Appell polynomials of class A^2, demonstrating their convergence properties and approximation capabilities through various classical and weighted measures.

Contribution

It develops a novel summation of Szász operators using Appell polynomials of class A^2 and establishes their convergence and approximation properties.

Findings

Verified Bohman-Korovkin's theorem for the new operators

Proved convergence in Lipschitz-type spaces and asymptotic formulas

Analyzed weighted modulus of continuity and derivatives of bounded variation

Abstract

This article contributes to the new summation of Sz\'asz operators with the help of Appell polynomials of class $A^{2}$. We verified Bohman-Korovkin's theorem and prove the convergence results like Lipschitz-type space, Voronvaskaja-type asymptotic formula, and modulus of continuity using the given operators. Furthermore, we have shown the weighted modulus of continuity and the derivative of bounded variation.