Nonlinear multivariate sampling Kantorovich operators: quantitative estimates in functional spaces

Çetin N., Costarelli D., Natale M., Vinti G.

Dolomites Research Notes on Approximation, vol.15, no.3, pp.12-25, 2022 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.14658/pupj-drna-2022-3-3
  • Journal Name: Dolomites Research Notes on Approximation
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.12-25
  • Ankara Haci Bayram Veli University Affiliated: Yes

Abstract

© 2022, Padova University Press. All rights reserved.In real world applications, signals can be suitably reconstructed by nonlinear procedures; this justifies the study of nonlinear approximation operators. In this paper, we prove some quantitative estimates for the nonlinear sampling Kantorovich operators in the multivariate setting using the modulus of smoothness of Lp (n ). The above results have been then extended to the general case of Orlicz spaces Lϕ (n ), so obtaining quantitative estimates in several instances of well-known and useful spaces.