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Applying Theorems on b -Metric Spaces to Differential and Integral Equations Through Connected-Image Contractions

Author

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  • 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)

  • Kanyuta Poochinapan

    (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)

  • 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
    Centre of Excellence in Mathematics, MHESI, Bangkok 10400, 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

This paper introduces a new concept of a connected-image set for a mapping, which extends the notion of edge-preserving properties with respect to mapping. We also present novel definitions of connected-image contractions, with a focus on fixed-point theorems involving auxiliary functions in b -metric spaces. The relationships between these mathematical concepts are explored, along with their applications to solving differential and integral equations. In particular, we discuss existence results for solving integral equations and second-order ordinary differential equations with inhomogeneous Dirichlet boundary conditions, as well as theorems related to contractions of the integral type.

Suggested Citation

  • Khuanchanok Chaichana & Kanyuta Poochinapan & Teeranush Suebcharoen & Phakdi Charoensawan, 2024. "Applying Theorems on b -Metric Spaces to Differential and Integral Equations Through Connected-Image Contractions," Mathematics, MDPI, vol. 12(24), pages 1-21, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3955-:d:1545127
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    References listed on IDEAS

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    1. HRITONENKO, Natali & YATSENKO, Yuri, 2009. "Integral equation of optimal replacement: analysis and algorithms," LIDAM Reprints CORE 2149, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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