Some New Results on Convergence, Weak w2-Stability and Data Dependence of Two Multivalued Almost Contractive Mappings in Hyperbolic Spaces

Austine Efut Ofem*, Jacob Ashiwere Abuchu, Reny George*, Godwin Chidi Ugwunnadi, Ojen Kumar Narain

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

In this article, we introduce a new mixed-type iterative algorithm for approximation of common fixed points of two multivalued almost contractive mappings and two multivalued mappings satisfying condition (Formula presented.) in hyperbolic spaces. We consider new concepts of weak (Formula presented.) -stability and data dependence results involving two multivalued almost contractive mappings. We provide examples of multivalued almost contractive mappings to show the advantage of our new iterative algorithm over some exiting iterative algorithms. Moreover, we prove several strong ∆-convergence theorems of our new algorithm in hyperbolic spaces. Furthermore, with another novel example, we carry out a numerical experiment to compare the efficiency and applicability of a new iterative algorithm with several leading iterative algorithms. The results in this article extend and improve several existing results from the setting of linear and CAT(0) spaces to hyperbolic spaces. Our main results also extend several existing results from the setting of single-valued mappings to the setting of multivalued mappings.

Original languageEnglish
Article number3720
JournalMathematics
Volume10
Issue number20
DOIs
Publication statusPublished - Oct 2022
Externally publishedYes

Keywords

  • data dependence
  • multivalued almost contractive mappings
  • multivalued mappings satisfying condition (E)
  • strong and ∆-convergence
  • weak w2-stability

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