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

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ASLAN İ.

FILOMAT, cilt.35, sa.8, ss.2731-2746, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 35 Sayı: 8
  • Basım Tarihi: 2021
  • Doi Numarası: 10.2298/fil2108731a
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.2731-2746
  • Anahtar Kelimeler: Approximation in phi-variation, discrete operators, generalized sampling series, rate of approximaiton, summability process, LINEAR INTEGRAL-OPERATORS, CONVERGENCE, SUMMABILITY, RESPECT
  • Hacettepe Üniversitesi Adresli: Evet

Özet

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.