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Existence of Common Fixed Points Through Auxiliary Contractions and Applications

Author

Listed:
  • Krittawit Limkul

    (Applied Mathematics and Statistics Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand)

  • Khuanchanok Chaichana

    (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
    Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand)

  • Raweerote Suparatulatorn

    (Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
    Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand
    Office of Research Administration, 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
    Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand)

Abstract

In this paper, we introduce a new type of contraction, an M -auxiliary contraction, by modifying existing concepts involving auxiliary functions. We establish existence and uniqueness results for common fixed points of the proposed contraction mapping under suitable conditions. Applications to fractional differential equations and ordinary differential equations are provided to demonstrate the effectiveness of the main theorem.

Suggested Citation

  • Krittawit Limkul & Khuanchanok Chaichana & Raweerote Suparatulatorn & Phakdi Charoensawan, 2025. "Existence of Common Fixed Points Through Auxiliary Contractions and Applications," Mathematics, MDPI, vol. 13(11), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1839-:d:1669346
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