New L-fuzzy fixed point techniques for studying integral inclusions

Mohammed Shehu Shagari, Trad Alotaibi, Hassen Aydi*, Ahmad Aloqaily, Nabil Mlaiki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

The survey of the available literature shows that a lot of important invariant point problems of Banach and Heilpern types have been examined in both metric and quasimetric spaces. However, a handful of the existing results employed the recent approaches of interpolative contractions. Therefore, based on the new idea of interpolation techniques in fixed point theory, this article studies new notions of L-fuzzy contractions and investigates conditions for the existence of L-fuzzy fixed points for such mappings. On the fact that fixed points of point-to-point mappings satisfying interpolative-type contraction are not always unique, whence making the concepts more fitted for invariant point results of crisp set-valued maps, new multi-valued analogues of the key findings put forward in this work are derived. Comparative illustrations, which indicate the preeminence of the results presented herein, are constructed. From application viewpoint, one of the theorems so obtained is employed to introduce new solvability conditions of Fredholm-type integral inclusions.

Original languageEnglish
Article number83
JournalJournal of Inequalities and Applications
Volume2024
Issue number1
DOIs
Publication statusPublished - Dec 2024
Externally publishedYes

Keywords

  • 46S40
  • 47H10
  • 54H25
  • Integral inclusion
  • Interpolation
  • L-fuzzy fixed point
  • L-fuzzy set

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