On the convergence, stability and data dependence results of the JK iteration process in Banach spaces

Kifayat Ullah, Naeem Saleem*, Hazrat Bilal, Junaid Ahmad, Muhammad Ibrar, Fahd Jarad*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

This article analyzes the JK iteration process with the class of mappings that are essentially endowed with a condition called condition (E). The convergence of the iteration toward a fixed point of a specific mapping satisfying the condition (E) is obtained under some possible mild assumptions. It is worth mentioning that the iteration process JK converges better toward a fixed point compared to some prominent iteration processes in the literature. This fact is confirmed by a numerical example. Furthermore, it has been shown that the iterative scheme JK is stable in the setting of generalized contraction. The data dependence result is also established. Our results are new in the iteration theory and extend some recently announced results of the literature.

Original languageEnglish
Article number20230101
JournalOpen Mathematics
Volume21
Issue number1
DOIs
Publication statusPublished - 1 Jan 2023
Externally publishedYes

Keywords

  • Banach space
  • Garcia-Falset map
  • JK- iteration
  • data dependence
  • stability
  • strong convergence
  • weak convergence

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