Approximation by Sampling-Type Nonlinear Discrete Operators in phi-Variation
FILOMAT, vol.35, no.8, pp.2731-2746, 2021 (SCI-Expanded, Scopus)
- 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.