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

Khuanchanok Chaichana, Kanyuta Poochinapan, Teeranush Suebcharoen and Phakdi Charoensawan ()
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Khuanchanok Chaichana: Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
Kanyuta Poochinapan: 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, 2024, vol. 12, issue 24, 1-21

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.

Keywords: connected-image contraction; fixed-point theorem; b-metric space; differential equation; integral equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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