We collect, improve, and generalize very recent results due to Mongkolkeha et al. (2014) in three directions: firstly, we study g-best proximity points; secondly, we employ more general test functions than can be found in that paper, which lets us prove best proximity results using different kinds of control functions; thirdly, we introduce and handle a weak version of the P-property. Our results can also be applied to the study of coincidence points between two mappings as a particular case. As a consequence, the contractive condition we introduce is more general than was used in the mentioned paper.
Poom Kumam. Antonio Francisco Roldán López de Hierro. "On Existence and Uniqueness of -Best Proximity Points under -Contractivity Conditions and Consequences." Abstr. Appl. Anal. 2014 (SI49) 1 - 14, 2014. https://doi.org/10.1155/2014/234027