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Citation - WoS: 13
Citation - Scopus: 14
The Existence of Optimal Approximate Solution Theorems for Generalized Α-Proximal Contraction Non-Self Mappings and Applications
(Springer international Publishing Ag, 2013) Karapinar, Erdal; Sintunavarat, Wutiphol
In 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.