Research Article

Multidimensional Kantorovich modifications of exponential sampling series

Published in: Quaestiones Mathematicae
Volume 46 , issue 1 , 2023 , pages: 57–72

DOI: 10.2989/16073606.2021.1992033

Author(s): Tuncer Acar Selcuk University, Turkey , Sadettin Kursun Selcuk University, Turkey , Metin Turgay Selcuk University, Turkey

Keywords: Primary: 41A25 , Secondary: 41A30 , 47A58 , Exponential sampling series , Kantorovich operators , rate of convergence , Voronovskaja type theorem

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Abstract

This paper is devoted to construction of multidimensional Kantorovich modifications of exponential sampling series, which allows to approximate suitable measurable functions by considering their mean values on just one section of the function involved. Approximation behaviour of newly constructed operators is investigated at continuity points for log-uniformly continuous functions. The rate of convergence of the series is presented for the same functions by means of logarithmic modulus of continuity. A Voronovskaja type theorem is also presented by means of Mellin derivatives.

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