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Approximation by nonlinear integral operators via summability process
Author(s) -
Aslan Ismail,
Duman Oktay
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800187
Subject(s) - mathematics , uniform norm , infimum and supremum , nonlinear system , norm (philosophy) , sequence (biology) , computation , convolution (computer science) , rate of convergence , convergence (economics) , mathematical analysis , algorithm , physics , quantum mechanics , channel (broadcasting) , electrical engineering , machine learning , biology , economic growth , political science , artificial neural network , computer science , law , economics , genetics , engineering
Abstract In this paper, we study the approximation properties of nonlinear integral operators of convolution‐type by using summability process. In the approximation, we investigate the convergence with respect to both the variation semi‐norm and the classical supremum norm. We also compute the rate of approximation on some appropriate function classes. At the end of the paper, we construct a specific sequence of nonlinear operators, which verifies the summability process. Some graphical illustrations and numerical computations are also provided.