Szász-Beta operators via Hermite Polynomial

Abstract

The aim of present article is to introduce the Szász-Beta operators in terms of Hermite Polynomial. We calculate some estimates and then discuss convergence theorems and order of approximation in terms of Korovkin theorem and first order modulus of smoothness respectively. Next, we study pointwise approximation results in terms of Peetre’s K-functional, second order modulus of smoothness, Lipschitz type space and rth order Lipschitz type maximal function. Lastly, weighted approximation results and statistical approximation theorems are proved.

Keywords

• Modulus of smoothness
• Szász operator
• Hermite Polynomial
• Order of approximation
• Rate of convergence