Approximation properties on q -Szasz-Mirakjan-Kantrovich Stancu type operators via Dunkl generalization

TL;DR

This paper investigates the approximation capabilities of q-Szasz-Mirakjan-Kantrovich-Stancu operators generated via Dunkl generalization, analyzing their convergence rates using classical tools and extending results to bivariate cases.

Contribution

It introduces new approximation properties and convergence rates for these operators based on Dunkl generalization and q-calculus, including bivariate extensions.

Findings

Operators approximate continuous functions with quantifiable rates.

Convergence is established via Korovkin's theorem.

Results extend to bivariate operators.

Abstract

This paper is devoted to study the approximation properties and rate of approximation of the Szasz-Mirakjan-Kantrovich-Stancu type polynomials generated by the Dunkl generalization of the exponential function with respect to q -calculus. We present approximation properties with the help of well-known Korovkin's theorem and determine the rat e of convergence in terms of classical modulus of continuity, the class of Lipschitz functions, Peetre's K-functional, and the second-order modulus of continuity. Moreover, we obtain the approximation results for Bivariate case for these operators