Research article

On dominated multivalued operators involving nonlinear contractions and applications

  • Received: 28 July 2023 Revised: 06 November 2023 Accepted: 07 November 2023 Published: 24 November 2023
  • MSC : 05C12, 39Bxx, 47H04, 47H10, 54H25

  • 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.

    Citation: Tahair Rasham, Najma Noor, Muhammad Safeer, Ravi Prakash Agarwal, Hassen Aydi, Manuel De La Sen. On dominated multivalued operators involving nonlinear contractions and applications[J]. AIMS Mathematics, 2024, 9(1): 1-21. doi: 10.3934/math.2024001

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  • 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.



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