Generalized Kantorovich forms of exponential sampling series
type: Item
instance of: scholarly article
title: Generalized Kantorovich forms of exponential sampling series
zbMATH Open document ID: 1497.41002
author: Ali Aral
author: Tuncer Acar
author: Sadettin Kursun
published in: Analysis and Mathematical Physics
publication date: 2022-03-18T00:00:00Z
review text: In this paper, authors introduce an interesting new family of operators by generalizing Kantorovich type of exponential sampling series by replacing integral means over exponentially spaced intervals with its more general analogue, Mellin Gauss Weierstrass singular integrals. Pointwise convergence of the family of operators is presented and a quantitative form of the convergence using a logarithmic modulus of continuity is given. Moreover, considering locally regular functions, an asymptotic formula in the sense of Voronovskaja is obtained. By introducing a new modulus of continuity for functions belonging to logarithmic weighted space of functions, a rate of convergence is obtained with some examples.
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 7493064
zbMATH Keywords: exponential sampling series
zbMATH Keywords: Kantorovich operators
zbMATH Keywords: Gauss-Weierstrass kernel
zbMATH Keywords: Mellin differential operator
zbMATH Keywords: pointwise convergence
zbMATH Keywords: asymptotic formula
MaRDI profile type: Publication
full work available at URL: s13324-022-00667-9
OpenAlex ID: W4220997341
Wikidata QID: Q115601041
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DOI: 10.1007/S13324-022-00667-9
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description: scientific article; zbMATH DE number 7493064