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Best Proximity Point for α‐ψ‐Proximal Contractive Multimaps

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Listed:
  • Muhammad Usman Ali
  • Tayyab Kamran
  • Naseer Shahzad

Abstract

We extend the notions of α‐ψ‐proximal contraction and α‐proximal admissibility to multivalued maps and then using these notions we obtain some best proximity point theorems for multivalued mappings. Our results extend some recent results by Jleli and those contained therein. Some examples are constructed to show the generality of our results.

Suggested Citation

  • Muhammad Usman Ali & Tayyab Kamran & Naseer Shahzad, 2014. "Best Proximity Point for α‐ψ‐Proximal Contractive Multimaps," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:181598
    DOI: 10.1155/2014/181598
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    References listed on IDEAS

    as
    1. Jack Markin & Naseer Shahzad, 2013. "Best Proximity Points for Relatively -Continuous Mappings in Banach and Hyperconvex Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-5, September.
    2. V. Pragadeeswarar & M. Marudai & P. Kumam & K. Sitthithakerngkiet, 2014. "The Existence and Uniqueness of Coupled Best Proximity Point for Proximally Coupled Contraction in a Complete Ordered Metric Space," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, May.
    3. Jack Markin & Naseer Shahzad, 2013. "Best Proximity Points for Relatively u‐Continuous Mappings in Banach and Hyperconvex Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. 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.
    5. 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).
    6. V. Pragadeeswarar & M. Marudai & P. Kumam & K. Sitthithakerngkiet, 2014. "The Existence and Uniqueness of Coupled Best Proximity Point for Proximally Coupled Contraction in a Complete Ordered Metric Space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    7. Muhammad Usman Ali & Tayyab Kamran & Wutiphol Sintunavarat & Phayap Katchang, 2013. "Mizoguchi‐Takahashi’s Fixed Point Theorem with α, η Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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