Dunkl-type generalization of the second kind beta operators via ( p , q ) $(p,q)$ -calculus

Abstract

Abstract The main purpose of this research article is to construct a Dunkl extension of ( p , q ) $(p,q)$ -variant of Szász–Beta operators of the second kind by applying a new parameter. We obtain Korovkin-type approximation theorems, local approximations, and weighted approximations. Further, we study the rate of convergence by using the modulus of continuity, Lipschitz class and Peetre’s K-functionals.

Keywords

• ( p , q ) $(p,q)$ -integers
• Dunkl exponential function
• ( p , q ) $(p,q)$ -beta operators
• Szász–Beta operators
• Weighted spaces