DOI: 10.24193/fpt-ro.2020.2.33

Authors: K. Fallahi and G. Soleimani Rad

Abstract: In this paper the existence and uniqueness of best proximity point for Reich-type contraction on b-metric spaces endowed with a graph is established. These results are significant, since we replace the condition of continuity of mapping with the condition of G-continuity of mapping and we consider b-metric spaces endowed with a graph instead of metric spaces, under which can be unified some theorems of the existing literature.

Key Words and Phrases: b-metric space, best proximity point, P-property, G-proximal.

2010 Mathematics Subject Classification: 41A52, 41A65, 05C40, 47H10.

Published on-line: July 1st, 2020.

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