Fixed points of non-linear multivalued graphic contractions with applications

Mohammed Shehu Shagari, Trad Alotaibi, Hassen Aydi*, Choonkil Park

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, a novel and more general type of sequence of non-linear multivalued mappings as well as the corresponding contractions on a metric space equipped with a graph is initiated. Fixed point results of a single-valued mapping and the new sequence of multivalued mappings are examined under suitable conditions. A non-trivial comparative illustration is provided to support the assumptions of our main theorem. A few important results in ɛ-chainable metric space and cyclic contractions are deduced as some consequences of the concepts obtained herein. As a result of our findings, new criteria for solving a broader form of Fredholm integral equation are established. An open problem concerning discretized population balance model whose solution may be investigated using any of the ideas proposed in this note is highlighted as a future assignment.

Original languageEnglish
Pages (from-to)20164-20177
Number of pages14
JournalAIMS Mathematics
Volume7
Issue number11
DOIs
Publication statusPublished - 2022
Externally publishedYes

Keywords

  • coincidence point
  • fixed point
  • non-linear multivalued graphic contraction
  • sequence of multivalued maps

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