On dominated multivalued operators involving nonlinear contractions and applications

Tahair Rasham*, Najma Noor, Muhammad Safeer, Ravi Prakash Agarwal, Hassen Aydi*, Manuel De La Sen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The objective of this research is to establish new results for set-valued dominated mappings that meet the criteria of advanced locally contractions in a complete extended b-metric space. Additionally, we intend to establish new fixed point outcomes for a couple of dominated multi-functions on a closed ball that satisfy generalized local contractions. In this study, we present novel findings for dominated maps in an ordered complete extended b-metric space. Additionally, we introduce a new concept of multi-graph dominated mappings on a closed ball within these spaces and demonstrate some original results for graphic contractions equipped with a graphic structure. To demonstrate the uniqueness of our new discoveries, we verify their applicability in obtaining a joint solution of integral and functional equations. Our findings have also led to modifications of numerous classical and contemporary results in existing research literature.

Original languageEnglish
Pages (from-to)1-21
Number of pages21
JournalAIMS Mathematics
Volume9
Issue number1
DOIs
Publication statusPublished - 2024
Externally publishedYes

Keywords

  • advanced locally contraction
  • dominated multi-functions
  • fixed point
  • functional equation
  • graph theory
  • integral equation
  • ordered extended b-metric space

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