'-BEST PROXIMITY POINT THEOREMS IN METRIC SPACES WITH APPLICATIONS IN PARTIAL METRIC SPACES

M. Imdad, H. N. Saleh, W. M. Alfaqih

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Abstract

In this paper, we introduce the notions of (F; '; )-proximal contraction and (F; '; )-weak proximal contraction for non-self mappings and utilize the same to prove some existence and uniqueness of '-best proximity point for such mappings. Some illustrative examples are also given to exhibit the utility of our results. As an application of the concept of '-best proximity point, we deduce some best proximity point theorems in the context of partial metric spaces.

Keywords

(F; '; )-proximal contraction, (F; '; )-weak proximal contraction, '-best proximity point, partial metric space.