Approximation by nonlinear integral operators via summability process. Issue 3 (3rd January 2020)

• Record Type: Journal Article
• Authors: Aslan, Ismail; Duman, Oktay
• Is Part Of: Mathematische Nachrichten. Volume 293:Issue 3(2020)
• Page Start: 430
• Page End: 448
• Publication Date: 2020-01-03
• Subjects: convolution type integral operators -- nonlinear integral operators -- summability process -- 40A25 -- 40C05 -- 41A25 -- 41A35 -- 41A36; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201800187
• Languages: English
• ISSNs: 0025-584X

Abstract

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.