Common Best Proximity Point Theorems for Generalized Dominating with Graphs and Applications in Differential Equations
In this paper, we initiate a concept of graph-proximal functions. Furthermore, we give a notion of being generalized Geraghty dominating for a pair of mappings. This permits us to establish the existence of and unique results for a common best proximity point of complete metric space. Additionally,...
Main Authors: | , , , , |
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Format: | Article |
Language: | English |
Published: |
MDPI AG
2024-01-01
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Series: | Mathematics |
Subjects: | |
Online Access: | https://www.mdpi.com/2227-7390/12/2/306 |
Summary: | In this paper, we initiate a concept of graph-proximal functions. Furthermore, we give a notion of being generalized Geraghty dominating for a pair of mappings. This permits us to establish the existence of and unique results for a common best proximity point of complete metric space. Additionally, we give a concrete example and corollaries related to the main theorem. In particular, we apply our main results to the case of metric spaces equipped with a reflexive binary relation. Finally, we demonstrate the existence of a solution to boundary value problems of particular second-order differential equations. |
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ISSN: | 2227-7390 |