Kantorovich variant of Stancu operators

Abstract

Stancu type operators play a crucial role in convergence estimates. The present article concerns the convergence estimates for certain Stancu type Kantorovich operators. We first establish some direct formulas giving the local approximation theorem, Voronovskaja type asymptotic formula, bound for the second central moment with some curtailment, and the global approximation theorem by means of modulus of continuity and the Ditzian-Totik Modulus of smoothness. We also study the difference estimates between Stancu-Bernstein operators and its Kantorovich variant. Further, we show the convergence of these operators by graphics to certain functions.