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Common Fixed Point Theorems for Novel Admissible Contraction with Applications in Fractional and Ordinary Differential Equations

Author

Listed:
  • Watchareepan Atiponrat

    (Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Pariwate Varnakovida

    (Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Thung Khru, Bangkok 10140, Thailand
    KMUTT Geospatial Engineering and Innovation Center, Faculty of Science, King Mongkut’s University of Technology Thonburi, Thung Khru, Bangkok 10140, Thailand)

  • Pharunyou Chanthorn

    (Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Teeranush Suebcharoen

    (Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Phakdi Charoensawan

    (Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

Abstract

In our work, we offer a novel idea of contractions, namely an ( α , β , γ ) P − contraction, to prove the existence of a coincidence point and a common fixed point in complete metric spaces. This leads us to an extension of previous results in the literature. Furthermore, we applied our acquired results to prove the existence of a solution for ordinary and fractional differential equations with integral-type boundary conditions.

Suggested Citation

  • Watchareepan Atiponrat & Pariwate Varnakovida & Pharunyou Chanthorn & Teeranush Suebcharoen & Phakdi Charoensawan, 2023. "Common Fixed Point Theorems for Novel Admissible Contraction with Applications in Fractional and Ordinary Differential Equations," Mathematics, MDPI, vol. 11(15), pages 1-20, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3370-:d:1208495
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    References listed on IDEAS

    as
    1. P. Charoensawan & W. Atiponrat, 2017. "Common Fixed Point and Coupled Coincidence Point Theorems for Geraghty’s Type Contraction Mapping with Two Metrics Endowed with a Directed Graph," Journal of Mathematics, Hindawi, vol. 2017, pages 1-9, November.
    2. Cholamjiak, Watcharaporn & Dutta, Hemen, 2022. "Viscosity modification with parallel inertial two steps forward-backward splitting methods for inclusion problems applied to signal recovery," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    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. Stoil I. Ivanov, 2020. "General Local Convergence Theorems about the Picard Iteration in Arbitrary Normed Fields with Applications to Super–Halley Method for Multiple Polynomial Zeros," Mathematics, MDPI, vol. 8(9), pages 1-11, September.
    Full references (including those not matched with items on IDEAS)

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