Weighted statistical approximation properties of univariate and bivariate λ-Kantorovich operators

Abstract

In this study, we consider statistical approximation properties of univariate and bivariate λ-Kantorovich operators. We estimate rate of weighted A-statistical convergence and prove a Voronovskajatype approximation theorem by a family of linear operators using the notion of weighted A-statistical convergence. We give some estimates for differences of λ-Bernstein and λ-Durrmeyer, and λ-Bernstein and λ-Kantorovich operators. We establish a Voronovskaja-type approximation theorem by weighted A-statistical convergence for the bivariate case.

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“…A new type -Bernstein operators have been introduced by Cai et al in [6] based on Bézier bases de…ned by Ye et al in [30]. We refer to [5,6,20,23,26] for recent studies about -Bernstein type operators and [13,14,28] for some Schuer type operators.…”

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