DOI: 10.24193/fpt-ro.2023.1.21

Authors: Asrifa Sultana

Abstract: We establish a unique best proximity point theorem for generalized set-valued contractions on metric spaces without involving the Hausdorff distance. This result subsumes and generalizes few important fixed point and best proximity point results for set-valued mappings. In particular, our result enables us to derive the Mizoguchi-Takahashi's fixed point result for closed valued map rather than closed and bounded valued. Moreover, we obtain a best proximity point result for maps satisfying Mizoguchi-Takahashi contractions uniformly locally.

Key Words and Phrases: Fixed point, best proximity point, set-valued nonself maps, metric space.

2010 Mathematics Subject Classification: 54H25, 47H10.

Published on-line: February 1st, 2023.

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