System of generalized variational-like inclusions involving (P,η) -accretive mapping and fixed point problems in real Banach spaces

Javad Balooee, Suliman Al-Homidan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This paper attempts to prove the Lipschitz continuity of the resolvent operator associated with a (P,η)-accretive mapping and compute an estimate of its Lipschitz constant. This is done under some new appropriate conditions that are imposed on the parameter and mappings involved in it; with the goal of approximating a common element of the solution set of a system of generalized variational-like inclusions and the fixed point set of a total asymptotically nonexpansive mapping in the framework of real Banach spaces. A new iterative algorithm based on the resolvent operator technique is proposed. Under suitable conditions, we prove the strong convergence of the sequence generated by our proposed iterative algorithm to a common element of the two sets mentioned above. The final section is dedicated to investigating and analyzing the notion of a generalized H(.,.)-accretive mapping introduced and studied by Kazmi et al. (Appl Math Comput 217:9679–9688, 2011). In this section, we provide some comments based on the relevant results presented in their work.

Original languageEnglish
Pages (from-to)1-33
Number of pages33
JournalArabian Journal of Mathematics
Volume13
Issue number1
DOIs
StatePublished - Apr 2024

Bibliographical note

Publisher Copyright:
© The Author(s) 2023.

Keywords

  • 47H05
  • 47H06
  • 47H09
  • 47J20
  • 47J22
  • 47J25
  • 49J40

ASJC Scopus subject areas

  • General Mathematics

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