A Note on Approximation Properties of Bernstein-type Operators via Some Summability Methods

Year 2024, Volume: 16 Issue: 2, 358 - 366, 31.12.2024

Dilek Soylemez Ozden , Emre Güven

Abstract

In this paper, we focus on two summability methods and investigate some applications of them for the Cheney-Sharma operators. We obtain approximation properties of the Cheney-Sharma operators via power series statistical convergence. We also analyze the convergence rates employing both the modulus of continuity and elements of the Lipschitz class. Additionally, we define r-th order generalization of the these operators which is linear but don't satisfy the positivity property and investigate approximation properties of these operators, via A-statistical convergence. We support our results with an example and a graph.

Keywords

Cheney-Sharma operators, power series statistical convergence, rate of convergence, rth order generalizations, A-statistical convergence

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