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 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.52280/pujm.2021.540201
  • Journal Name: PUNJAB UNIVERSITY JOURNAL OF MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.75-87
  • Keywords: Convergence, Stable, Jungck-Kirk iteration method, DATA DEPENDENCE, FIXED-POINTS, APPROXIMATION, MAPPINGS
  • Yıldız Technical University Affiliated: Yes

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.