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Some Common Fixed Point Results in Modular Ultrametric Space Using Various Contractions and Their Application to Well-Posedness

Author

Listed:
  • Yahya Almalki

    (Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia)

  • Balaanandhan Radhakrishnan

    (Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, Tamilnadu, India)

  • Uma Jayaraman

    (Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, Tamilnadu, India)

  • Kandhasamy Tamilvanan

    (Department of Mathematics, Faculty of Science & Humanities, R.M.K. Engineering College, Tiruvallur 601206, Tamil Nadu, India)

Abstract

The aim of this study is to prove the existence and uniqueness of fixed point and common fixed point theorems for self-mappings in modular ultrametric spaces. These theorems are proved under varying contractive circumstances and without the property of spherical completeness. As a consequence, the examples of fixed point and common fixed point problems are correctly formulated. As an application, the well-posedness of a common fixed point problem is proved. This study expands on prior research in modular ultrametric space to provide a more comprehensive understanding of such spaces using generalized contraction.

Suggested Citation

  • Yahya Almalki & Balaanandhan Radhakrishnan & Uma Jayaraman & Kandhasamy Tamilvanan, 2023. "Some Common Fixed Point Results in Modular Ultrametric Space Using Various Contractions and Their Application to Well-Posedness," Mathematics, MDPI, vol. 11(19), pages 1-18, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4077-:d:1247923
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    References listed on IDEAS

    as
    1. Kandhasamy Tamilvanan & Abdulaziz M. Alanazi & Maryam Gharamah Alshehri & Jeevan Kafle, 2021. "Hyers-Ulam Stability of Quadratic Functional Equation Based on Fixed Point Technique in Banach Spaces and Non-Archimedean Banach Spaces," Mathematics, MDPI, vol. 9(20), pages 1-15, October.
    2. Syed Abdul Mohiuddine & Kandhasamy Tamilvanan & Mohammad Mursaleen & Trad Alotaibi, 2022. "Stability of Quartic Functional Equation in Modular Spaces via Hyers and Fixed-Point Methods," Mathematics, MDPI, vol. 10(11), pages 1-22, June.
    3. Kandhasamy Tamilvanan & Ali H. Alkhaldi & Jyotsana Jakhar & Renu Chugh & Jagjeet Jakhar & John Michael Rassias, 2023. "Ulam Stability Results of Functional Equations in Modular Spaces and 2-Banach Spaces," Mathematics, MDPI, vol. 11(2), pages 1-23, January.
    Full references (including those not matched with items on IDEAS)

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    1. Kandhasamy Tamilvanan & Ali H. Alkhaldi & Jyotsana Jakhar & Renu Chugh & Jagjeet Jakhar & John Michael Rassias, 2023. "Ulam Stability Results of Functional Equations in Modular Spaces and 2-Banach Spaces," Mathematics, MDPI, vol. 11(2), pages 1-23, January.

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