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

Watchareepan Atiponrat, Pariwate Varnakovida, Pharunyou Chanthorn, Teeranush Suebcharoen and Phakdi Charoensawan ()
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Watchareepan Atiponrat: Advanced Research Center for Computational Simulation, 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
Pharunyou Chanthorn: Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
Teeranush Suebcharoen: 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, 2023, vol. 11, issue 15, 1-20

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.

Keywords: Geraghty function; admissibility; contraction; common fixed point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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