Approximation properties of the Stancu type Dunkl generalization of the Kantorovich-Sz\'asz-Mirakjan-operators via q-calculus

TL;DR

This paper introduces a new class of Dunkl-generalized q-Kantorovich-Szász-Mirakjan operators, analyzing their approximation capabilities and convergence rates using various mathematical tools and theorems.

Contribution

It constructs and studies the approximation properties of Stancu type Dunkl q-operators, extending existing operators with new convergence and rate results.

Findings

Operators effectively approximate functions in Lipschitz class.

Convergence rates are quantified using modulus of continuity.

Results include classical and weighted approximation estimates.

Abstract

In this paper we construct Stancu type q-Kantrovich-Sz\'asz-Mirakjan operators generated by Dunkl generalization of the exponential function. We obtain some approximation results using the Korovkin approximation theorem and the weighted Korovkin-type theorem for these operators. We also study convergence properties by using the modulus of continuity and the rate of convergence of these operators for functions belonging to the Lipschitz class. Furthermore, we obtain the rate of convergence in terms of the classical, second order, and weighted modulus of continuity.