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

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.

Keywords:

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

Author contributions

Supervision, Parin Chaipunya; Writing – original draft, Sakan Termkaew; Review & editing, Dhananjay Gopal; Review & editing, Poom Kumam.

Acknowledgements

The authors thank Editor-in-Chief/Area Editors and Referee(s) for their valuable comments and suggestions, which were very much useful to improve the paper significantly.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. The authors acknowledge the financial support provided by ‘Mid-Career Research Grant’ [N41A640089]. The first author was supported by the Petchra Pra Jom Klao Ph.D. Research Scholarship from King Mongkut's University of Technology Thonburi [Grant No.51/2563]. This work was completed while the third author (Dr. Gopal) was visiting Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok, Thailand, during 14 June–22 June, 2022. He thanks Professor Poom Kumam and the University for their hospitality and support. He also thank to administration of GGV Bilaspur. Thus research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund under project number FRB660073/0164.