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In this paper, we consider Kantorovich extension of generalized Bernstein–Schurer operators depending on a non-negative integer parameter. We prove approximation theorems in the space of continuous functions and \(L_{p}\) -space. Moreover, we obtain some estimates for the rate of convergence by using modulus of continuity and \(L_{p}\) modulus of smoothness of the first order.

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Generalized Kantorovich–Schurer-Type Operators

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  • 发表日期：

    2025年

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  • Nursel Çetin

摘要

In this paper, we consider Kantorovich extension of generalized Bernstein–Schurer operators depending on a non-negative integer parameter. We prove approximation theorems in the space of continuous functions and \(L_{p}\) -space. Moreover, we obtain some estimates for the rate of convergence by using modulus of continuity and \(L_{p}\) modulus of smoothness of the first order.