Inertial Halpern-type method for solving split feasibility and fixed point problems via dynamical stepsize in real Banach spaces

G. C. Ugwunnadi, H. A. Abass*, M. Aphane, O. K. Oyewole

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

In this paper, we introduce a modified Halpern inertial method for approximating solutions of split feasibility problem and fixed point problem of Bregman strongly nonexpansive mappings in the framework of p-uniformly convex and uniformly smooth real Banach spaces. We establish a strong convergence result for the sequence generated by our iterative scheme under some mild conditions without the computation of the operator norm. We state some consequences and present some examples to show the efficiency and implementation of our proposed method. The result discussed in this paper extends and generalizes many recent results in this direction. Our result extends and complements some related results in literature.

Original languageEnglish
Pages (from-to)307-330
Number of pages24
JournalAnnali dell'Universita di Ferrara
Volume70
Issue number2
DOIs
Publication statusPublished - Jun 2024
Externally publishedYes

Keywords

  • 47H06
  • 47H09
  • 47J05
  • 47J25
  • Bregman strongly nonexpansive
  • Fixed point problem
  • Inertial method
  • Iterative scheme
  • Split feasibility problem

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