Convergence of Jungck-Kirk Type Iteration Method with Applications

MALDAR S., KARAKAYA V.

PUNJAB UNIVERSITY JOURNAL OF MATHEMATICS, cilt.54, sa.2, ss.75-87, 2022 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 54 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.52280/pujm.2021.540201
  • Dergi Adı: PUNJAB UNIVERSITY JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.75-87
  • Anahtar Kelimeler: Convergence, Stable, Jungck-Kirk iteration method, DATA DEPENDENCE, FIXED-POINTS, APPROXIMATION, MAPPINGS
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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.