Approximation by Sampling-Type Nonlinear Discrete Operators in phi-Variation

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FILOMAT, vol.35, no.8, pp.2731-2746, 2021 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 8
  • Publication Date: 2021
  • Doi Number: 10.2298/fil2108731a
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.2731-2746
  • Keywords: Approximation in phi-variation, discrete operators, generalized sampling series, rate of approximaiton, summability process, LINEAR INTEGRAL-OPERATORS, CONVERGENCE, SUMMABILITY, RESPECT
  • Open Archive Collection: AVESIS Open Access Collection
  • Hacettepe University Affiliated: Yes

Abstract

In the present paper, our purpose is to obtain a nonlinear approximation by using convergence in phi-variation. Angeloni and Vinti prove some approximation results considering linear sampling-type discrete operators. These types of operators have close relationships with generalized sampling series. By improving Angeloni and Vinti's one, we aim to get a nonlinear approximation which is also generalized by means of summability process. We also evaluate the rate of approximation under appropriate Lipschitz classes of phi-absolutely continuous functions. Finally, we give some examples of kernels, which fulfill our kernel assumptions.