On Existence and Uniqueness of g -Best Proximity Points under φ , θ , α , g -Contractivity Conditions and Consequences

Abstract

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.