Karapınar, ErdalKarapinar, ErdalSintunavarat, WutipholMathematics2024-07-052024-07-052013131687-181210.1186/1687-1812-2013-3232-s2.0-84901763514https://doi.org/10.1186/1687-1812-2013-323https://hdl.handle.net/20.500.14411/258KARAPINAR, ERDAL/0000-0002-6798-3254; Sintunavarat, Wutiphol/0000-0002-0932-1332In this paper, we investigate the sufficient conditions to find a best proximity point for a certain class of non-self mappings. It is well known that optimization problems can be transformed to the problems of the existence of a best proximity point. Hence, improvement in the best proximity point theory implicitly develops the theory of optimization. Our presented results generalize, extent and improve various well-known results on the topic in the literature. In particular, we consider some applications of our results to the best proximity point theorems on a class of metric spaces endowed with an arbitrary binary relation which involves the partially ordered metric spaces.eninfo:eu-repo/semantics/openAccessapproximately compactbest proximity pointbinary relationgeneralized alpha-proximal contraction of the first kindgeneralized alpha-proximal contraction of the second kindArticleWOS:000328702300002