Total asymptotically nonexpansive mappings and generalized variational-like inclusion problems in semi-inner product spaces

Javad Balooee, Suliman Al-Homidan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This paper focuses on investigating the problem of finding a common element of the set of solutions of a generalized nonlinear implicit variational-like inclusion problem involving an (Formula presented.) -maximal m-relaxed monotone mapping in the sense of L.-G.-s.i.p. and the set of fixed points of a total asymptotically nonexpansive mapping. To achieve such a purpose, a new iterative algorithm is constructed. Applying the concepts of graph convergence and generalized resolvent operator associated with an (Formula presented.) -maximal m-relaxed monotone mapping in the sense of L.-G.-s.i.p. As an application of the obtained equivalence relationship, the strong convergence of the sequence generated by our proposed iterative algorithm to a point belonging to the intersection of the two sets mentioned above is proved.

Original languageEnglish
Pages (from-to)741-792
Number of pages52
JournalOptimization
Volume73
Issue number3
DOIs
StatePublished - 2024

Bibliographical note

Publisher Copyright:
© 2022 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

  • (A,η)-maximal m-relaxed monotone mapping
  • Total asymptotically nonexpansive mapping
  • convergence analysis
  • fixed point problem
  • graph convergence
  • iterative algorithm
  • resolvent operator technique
  • semi-inner product spaces
  • variational-like inclusions

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics
  • Management Science and Operations Research

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