Weighted approximations by sampling type operators: recent and new results

Year 2024, Volume: 7 Issue: 3, 114 - 125, 15.09.2024

Osman Alagoz

https://doi.org/10.33205/cma.1528004

Abstract

In this paper, we collect some recent results on the approximation properties of generalized sampling operators and Kantorovich operators, focusing on pointwise and uniform convergence, rate of convergence, and Voronovskaya-type theorems in weighted spaces of functions. In the second part of the paper, we introduce a new generalization of sampling Durrmeyer operators including a special function $\rho$ which satisfies certain assumptions. For the family of newly constructed operators, we obtain pointwise convergence, uniform convergence and rate of convergence for functions belonging to weighted spaces of functions.

Keywords

Sampling series, generalized sampling operator, Kantorovich operator, Durrmeyer type sampling operator, weighted approximation

Supporting Institution

TUBITAK

Thanks

This study was supported by Scientific and Technological Research Council of Turkey (TUBITAK) under the Grant Number 119F263. The author thank to TUBITAK for their supports.

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