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

Year 2020, Volume: 10 Issue: 1, 190 - 200, 01.01.2020

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

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.

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