Convergence of Jungck-Kirk Type Iteration Method with Applications


MALDAR S., KARAKAYA V.

PUNJAB UNIVERSITY JOURNAL OF MATHEMATICS, vol.54, no.2, pp.75-87, 2022 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.52280/pujm.2021.540201
  • Title of Journal : PUNJAB UNIVERSITY JOURNAL OF MATHEMATICS
  • Page Numbers: pp.75-87
  • Keywords: Convergence, Stable, Jungck-Kirk iteration method, DATA DEPENDENCE, FIXED-POINTS, APPROXIMATION, MAPPINGS

Abstract

The aim of this article is to define a new Jungck-Kirk type iteration method and to examine the convergence result under appropriate conditions together with other Jungck-Kirk type iteration methods in the literature. It is also to analyze whether the newly defined iteration method is stable. In addition, it has been shown through numerical examples that the new iteration method has a better convergence rate than the others. Finally, to show the validity of convergence and stability results, some examples are given. The results obtained in this paper may be interpreted as a refinement and improvement of the previously known results.