Existence of Common Fixed Points Through Auxiliary Contractions and Applications

Krittawit Limkul, Khuanchanok Chaichana (), Raweerote Suparatulatorn and Phakdi Charoensawan ()
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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
Raweerote Suparatulatorn: Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
Phakdi Charoensawan: Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand

Mathematics, 2025, vol. 13, issue 11, 1-16

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.

Keywords: M-auxiliary contraction; fixed-point theorem; fractional differential equation; ordinary differential equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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