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

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  • Poom Kumam
  • Antonio Francisco Roldán López de Hierro

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.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:234027
DOI: 10.1155/2014/234027
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