Coupled Coincidence Best Proximity Point Theorems on a Metric Space with a Graph

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Published: 2025-06-15
Keywords:
Coupled best proximity point, coupled coincidence point, coupled common fixed point, metric space with a graph

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Satyaj Tiwari
a:1:{s:5:"en_US";s:80:"Shri Shankaracharya Institute of Professional Management and Technology, Raipur ";}
Suchitra Dey
Shri Shankracharya Institute of Professional management and Technology, Raipur

Abstract

In this paper, we have established the results by introducing the new notion of a coupled coincidence best proximity point instead of the coupled best proximity point in the setting of a partially ordered complete metric space with graph. Our paper is inspired by the work of D. Eshi, P. K Das and P. Debnath1.

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Vol. 29 No. 2 (2025): Table of Content

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite

1.
Coupled Coincidence Best Proximity Point Theorems on a Metric Space with a Graph. J. Int. Acad. Phys. Sci. [Internet]. 2025 Jun. 15 [cited 2026 Oct. 23];29(2):61-72. Available from: http://www.iaps.org.in/journal/index.php/journaliaps/article/view/1027

References

D. Eshi, P. Das and P. Debnath; Coupled coincidence and coupled common fixed point theorems on a metric space with a graph, Fixed Point Theory and Applications, (2016), 37.

W. Sintunavarat, P. Kumam; Coupled best proximity point theoreminmetric spaces, Fixed Point Theory and Applications, (2012), 93.

V. Lakshmikantham, L. Cˇiricˇ; Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., Theory Methods Appl., 70(12) (2009),4341-4349.

J. Jachymski; The contraction principle for mappings on a metric space with a graph, Proc. American Math. Soc., 136(4) (2008), 1359-1373.

C. Chifu, G. Petrusel; New results on coupled fixed point theory in metric spaces endowed with a directed graph, Fixed Point Theory Appl., 151 (2014).