On Paltanea operator linking Hermite polynomials

Abstract

In this article, we introduce a new variant of the Paltanea operator based on modified Hermite ˘ polynomials of two variables. We establish several approximation properties for this operator including Voronovskaja theorem in weighted space and illustrate its convergence both numerically and graphically. Additionally, we capture a new interesting operator based on a composition method and then we established asymptotic formula for composition operator. We also study its convergence in terms of first and second order modulus of continuity and present a theorem based on difference estimates.