Open AccessApproximation by sampling-type nonlinear discrete operators in φ-variation
Author(s) -
İsmail Aslan
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2108731a
Subject(s) - mathematics , lipschitz continuity , nonlinear system , type (biology) , rate of convergence , kernel (algebra) , convergence (economics) , sampling (signal processing) , variation (astronomy) , series (stratigraphy) , mathematical analysis , pure mathematics , ecology , channel (broadcasting) , paleontology , physics , filter (signal processing) , quantum mechanics , economic growth , computer science , astrophysics , electrical engineering , economics , computer vision , biology , engineering
In the present paper, our purpose is to obtain a nonlinear approximation by using convergence in ?-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 ?-absolutely continuous functions. Finally, we give some examples of kernels, which fulfill our kernel assumptions.