Convergence of generalized sampling series in weighted spaces

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Acar T., ALAGÖZ O., Aral A., Costarelli D., Turgay M., Vinti G.

Demonstratio Mathematica, vol.55, no.1, pp.153-162, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 55 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.1515/dema-2022-0014
  • Journal Name: Demonstratio Mathematica
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Linguistic Bibliography, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.153-162
  • Keywords: generalized sampling operators, quantitative order of approximation, Voronovskaja-type theorem, weighted modulus of continuity, weighted spaces
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

© 2022 Tuncer Acar et al., published by De Gruyter.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.