DOI: 10.24193/fpt-ro.2024.1.12

Authors: S. Laha, S. Som, L.K. Dey and H. Huang

Abstract: Let X be an arbitrary topological space and g : X × X → ℝ be a real valued continuous function defined on X × X. In this article, we introduce two notions like topologically Berinde weak proximal contraction and topologically proximal weakly contractive mapping with respect to g. We explore sufficient conditions for the existence and uniqueness of best proximity points for these classes of mappings. Moreover, in the last part of the paper, we show that the best proximity point theorem for topologically proximal weakly contractive mapping can be deduced from some fixed point theorems in topological spaces.

Key Words and Phrases: Best proximity point, fixed point, topological space, Berinde weak proximal contraction mapping, approximatively compact.

2010 Mathematics Subject Classification: 54H25, 47H10, 46A50.

Published on-line: February 1st, 2024.

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