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Relation-Theoretic Weak Contractions and Applications

Author

Listed:
  • Asik Hossain

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India)

  • Aftab Alam

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
    Current address: Centre of Professional Courses, Aligarh Muslim University, Aligarh 202002, India.)

  • Salvatore Sessa

    (Department of Architecture, University of Naples Federico II, Via Toledo 402, 80134 Naples, Italy)

  • Qamrul Haque Khan

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India)

Abstract

In this article, we discuss the relation-theoretic aspects of weakly contractive mappings to prove fixed point results in the setting of metric spaces endowed with a certain binary relation. We also provide an example and an application to validate of our results. The results proved herewith unify, generalize, improve, extend, sharpen, subsume and enrich some well-known fixed point theorems of the existing literature.

Suggested Citation

  • Asik Hossain & Aftab Alam & Salvatore Sessa & Qamrul Haque Khan, 2023. "Relation-Theoretic Weak Contractions and Applications," Mathematics, MDPI, vol. 11(9), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:1976-:d:1129935
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    References listed on IDEAS

    as
    1. Maher Berzig & Erdal Karapınar & Antonio-Francisco Roldán-López-de-Hierro, 2014. "Discussion on Generalized-( α ψ , β )-Contractive Mappings via Generalized Altering Distance Function and Related Fixed Point Theorems," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, February.
    2. Mihai Turinici, 2014. "Contractive Operators in Relational Metric Spaces," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Handbook of Functional Equations, edition 127, pages 419-458, Springer.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Khursheed J. Ansari & Salvatore Sessa & Aftab Alam, 2023. "A Class of Relational Functional Contractions with Applications to Nonlinear Integral Equations," Mathematics, MDPI, vol. 11(15), pages 1-11, August.
    2. Doaa Filali & Mohammad Dilshad & Mohammad Akram, 2024. "Weak ψ -Contractions on Directed Graphs with Applications to Integral Equations," Mathematics, MDPI, vol. 12(17), pages 1-12, August.
    3. Doaa Filali & Mohammad Akram & Mohammad Dilshad, 2023. "An Extension of Strict Almost Contractions Employing Control Function and Binary Relation with Applications to Boundary Value Problems," Mathematics, MDPI, vol. 11(19), pages 1-11, September.

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