A contribution to best proximity point theory and an application to partial differential equation

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Publication Details

Author list: Termkaew, Sakan; Chaipunya, Parin; Gopal, Dhananjay; Kumam, Poom;

Publisher: Taylor and Francis Group

Publication year: 2023

ISSN: 0233-1934

eISSN: 1029-4945

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85150897099&doi=10.1080%2f02331934.2023.2191620&partnerID=40&md5=a7f9576df86229b13ed52590ee463091

Languages: English-Great Britain (EN-GB)

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Abstract

In this work, the main discussion centres on avoiding the use of triangle inequality while proving Cauchy sequence to establish best proximity point theorems for single valued as well as multivalued non-self mappings. We prove such best proximity point theorems in the setting of non-triangular metric spaces and elaborate through examples. In this process host of the existing best proximity results are generalized and improved. To arouse further interest in the subject, we connect this work in solving a specific type of partial differential equation problem. © 2023 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

Best proximal points, non-triangular metric spaces, partial differential equation