Approximation by a generalized class of Dunkl type Szász operators based on post quantum calculus

Abstract

Abstract The main purpose of this paper is to introduce a generalized class of Dunkl type Szász operators via post quantum calculus on the interval [12,∞) $[ \frac{1}{2},\infty )$. This type of modification allows a better estimation of the error on [12,∞) $[ \frac{1}{2},\infty ) $ rather than [0,∞) $[ 0,\infty )$. We establish Korovkin type result in weighted spaces and also study approximation properties with the help of modulus of continuity of order one, Lipschitz type maximal functions, and Peetre’s K-functional. Furthermore, we estimate the degrees of approximations of the operators by modulus of continuity of order two.

Keywords

• ( p , q ) $(p,q)$ -integers
• Dunkl analogue
• Dunkl generalization of exponential function
• Szász operator
• Lipschitz type maximal functions
• Peetre’s K-functional