BEST PROXIMITY POINT RESULTS FOR PROXIMAL CONTRACTION IN TOPOLOGICAL SPACES.

Let X be an arbitrary topological space and g : X x X → R be a real valued continuous function defined on X 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. [ABSTRACT FROM AUTHOR]