Convergence of generalized sampling series in weighted spaces

Acar Tuncer; Alagöz Osman; Aral Ali; Costarelli Danilo; Turgay Metin; Vinti Gianluca

doi:10.1515/dema-2022-0014

Demonstratio Mathematica (May 2022)

Convergence of generalized sampling series in weighted spaces

Acar Tuncer,
Alagöz Osman,
Aral Ali,
Costarelli Danilo,
Turgay Metin,
Vinti Gianluca

Affiliations

Acar Tuncer: Department of Mathematics, Selcuk University, Faculty of Science, Selcuklu, 42003, Konya, Turkey
Alagöz Osman: Department of Mathematics, Bilecik Seyh Edebali University, Faculty of Science, Bilecik, Turkey
Aral Ali: Department of Mathematics, Kirikkale University, Faculty of Science and Arts, Yahsihan, 71450, Kirikkale, Turkey
Costarelli Danilo: Department of Mathematics and Computer Science, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, Italy
Turgay Metin: Department of Mathematics, Selcuk University, Faculty of Science, Selcuklu, 42003, Konya, Turkey
Vinti Gianluca: Department of Mathematics and Computer Science, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, Italy

DOI: https://doi.org/10.1515/dema-2022-0014
Journal volume & issue: Vol. 55, no. 1
pp. 153 – 162

Abstract

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The present paper deals with an extension of approximation properties of generalized sampling series to weighted spaces of functions. A pointwise and uniform convergence theorem for the series is proved for functions belonging to weighted spaces. A rate of convergence by means of weighted moduli of continuity is presented and a quantitative Voronovskaja-type theorem is obtained.

Published in Demonstratio Mathematica

ISSN: 2391-4661 (Online)
Publisher: De Gruyter
Country of publisher: Poland
LCC subjects: Science: Mathematics
Website: https://www.degruyter.com/journal/key/dema/html

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