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Fixed Point Results for Hybrid Rational Contractions under a New Compatible Condition with an Application

Author

Listed:
  • Xiaolan Liu

    (College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
    Artificial Intelligence Key Laboratory of Sichuan Province, Zigong 643000, China
    South Sichuan Center for Applied Mathematics, Zigong 643000, China)

  • Mi Zhou

    (School of Science and Techology, University of Sanya, Sanya 572022, China
    Center for Mathematical Reaserch, University of Sanya, Sanya 572022, China
    Academician Guoliang Chen Team Innovation Center, University of Sanya, Sanya 572022, China
    Academician Chunming Rong Workstation, University of Sanya, Sanya 572022, China)

  • Arslan Hojat Ansari

    (Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj 6915136111, Iran
    Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria 0204, South Africa)

  • Naeem Saleem

    (Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria 0204, South Africa
    Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan)

  • Mukesh Kumar Jain

    (Jawahar Navodaya Vidyalaya, Udalguri 784509, India)

Abstract

In this scholarly discourse, we present proof of the existence of unique fixed points in b -metric spaces for hybrid rational contractions. Moreover, we establish a common fixed point theorem for four self-mappings, assuming S -compatibility for two pairs of self-mappings within the framework of b -metric spaces. As a practical demonstration of the aforementioned results, we apply them to a type of integral equation and derive a theorem that guarantees the existence of solutions.

Suggested Citation

  • Xiaolan Liu & Mi Zhou & Arslan Hojat Ansari & Naeem Saleem & Mukesh Kumar Jain, 2023. "Fixed Point Results for Hybrid Rational Contractions under a New Compatible Condition with an Application," Mathematics, MDPI, vol. 12(1), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:121-:d:1310289
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    References listed on IDEAS

    as
    1. Erdal Karapınar & Andreea Fulga, 2019. "New Hybrid Contractions on b -Metric Spaces," Mathematics, MDPI, vol. 7(7), pages 1-15, June.
    2. Mi Zhou & Xiao-Lan Liu & Arslan Hojat Ansari & Mukesh Kumar Jain & Jia Deng & Naeem Saleem, 2021. "Common Fixed Point Theorems via Inverse Ck− Class Functions in Metric Spaces," Journal of Mathematics, Hindawi, vol. 2021, pages 1-25, April.
    3. Gerald Jungck, 1986. "Compatible mappings and common fixed points," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 9, pages 1-9, January.
    4. Mohammad Ali Alghamdi & Stojan Radenović & Naseer Shahzad, 2012. "On Some Generalizations of Commuting Mappings," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-6, January.
    Full references (including those not matched with items on IDEAS)

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