Convergence in Phi-Variation and Rate of Approximation for Nonlinear Integral Operators Using Summability Process


ASLAN İ.

MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.18, no.1, 2020 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.1007/s00009-020-01623-2
  • Journal Name: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, MathSciNet, zbMATH, DIALNET
  • Keywords: Summability process, nonlinear integral operators, convolution-type integral operators, bounded phi-variation, rate of approximation, ACCELERATION, RESPECT

Abstract

We investigate the approximation properties of nonlinear integral operators of the convolution type. In this approximation, we use functions of bounded variation based on the appropriate functionals. To get more general results, we consider Bell-type summability methods in the approximation. Moreover, we examine the rate of approximation. Then, using summability methods, we obtain a characterization for absolute continuity. Our examples at the end of the paper clearly demonstrate why we used summability methods rather than convergence in the conventional sense.