Summability on Mellin-type nonlinear integral operators

ASLAN İ., Duman O.

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, vol.30, no.6, pp.492-511, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 6
  • Publication Date: 2019
  • Doi Number: 10.1080/10652469.2019.1594209
  • Journal Name: INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.492-511
  • Keywords: Summability process, nonlinear integral operators, convolution-type integral operators, Mellin-type integral operators, bounded variation, CONVERGENCE, APPROXIMATION
  • Hacettepe University Affiliated: Yes

Abstract

In this study, approximation properties of the Mellin-type nonlinear integral operators defined on multivariate functions are investigated. In order to get more general results than the classical aspects, we mainly use the summability methods defined by Bell. Considering the Haar measure with variation semi-norm in Tonelli's sense, we approach to the functions of bounded variation. Similar results are also obtained for uniformly continuous and bounded functions. Using suitable function classes we investigate the rate of convergence in the approximation. Finally, we give a non-trivial application verifying our approach.