On dominated multivalued operators involving nonlinear contractions and applications

Abstract

<abstract> <p>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 <italic>b</italic>-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 <italic>b</italic>-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.</p> </abstract>