Approximation by nonlinear integral operators via summability process

ASLAN İ., DUMAN O.

MATHEMATISCHE NACHRICHTEN, vol.293, no.3, pp.430-448, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 293 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.1002/mana.201800187
  • Journal Name: MATHEMATISCHE NACHRICHTEN
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.430-448
  • Keywords: convolution type integral operators, nonlinear integral operators, summability process, CONVERGENCE, ACCELERATION, SEQUENCES
  • Hacettepe University Affiliated: Yes

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.