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

Author

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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.

Suggested Citation

  • Poom Kumam & Antonio Francisco Roldán López de Hierro, 2014. "On Existence and Uniqueness of g‐Best Proximity Points under (φ, θ, α, g)‐Contractivity Conditions and Consequences," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:234027
    DOI: 10.1155/2014/234027
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    References listed on IDEAS

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    1. Maryam A. Alghamdi & Naseer Shahzad & Francesca Vetro, 2013. "Best Proximity Points for Some Classes of Proximal Contractions," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, September.
    2. Chirasak Mongkolkeha & Chayut Kongban & Poom Kumam, 2014. "Existence and Uniqueness of Best Proximity Points for Generalized Almost Contractions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, March.
    3. Chirasak Mongkolkeha & Chayut Kongban & Poom Kumam, 2014. "Existence and Uniqueness of Best Proximity Points for Generalized Almost Contractions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Maryam A. Alghamdi & Naseer Shahzad & Francesca Vetro, 2013. "Best Proximity Points for Some Classes of Proximal Contractions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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