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Best Proximity Point Results for Modified α‐ψ‐Proximal Rational Contractions

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  • N. Hussain
  • M. A. Kutbi
  • P. Salimi

Abstract

We first introduce certain new concepts of α‐η‐proximal admissible and α‐η‐ψ‐rational proximal contractions of the first and second kinds. Then we establish certain best proximity point theorems for such rational proximal contractions in metric spaces. As an application, we deduce best proximity and fixed point results in partially ordered metric spaces. The presented results generalize and improve various known results from best proximity point theory. Several interesting consequences of our obtained results are presented in the form of new fixed point theorems which contain famous Banach′s contraction principle and some of its generalizations as special cases. Moreover, some examples are given to illustrate the usability of the obtained results.

Suggested Citation

  • N. Hussain & M. A. Kutbi & P. Salimi, 2013. "Best Proximity Point Results for Modified α‐ψ‐Proximal Rational Contractions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:927457
    DOI: 10.1155/2013/927457
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    References listed on IDEAS

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    1. Ravi P. Agarwal & Nawab Hussain & Mohamed-Aziz Taoudi, 2012. "Fixed Point Theorems in Ordered Banach Spaces and Applications to Nonlinear Integral Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, July.
    2. Mohamed Jleli & Erdal Karapınar & Bessem Samet, 2013. "Best Proximity Points for Generalized α‐ψ‐Proximal Contractive Type Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    3. M. A. Kutbi & Jamshaid Ahmad & Nawab Hussain & Muhammad Arshad, 2013. "Common Fixed Point Results for Mappings with Rational Expressions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Ravi P. Agarwal & Nawab Hussain & Mohamed-Aziz Taoudi, 2012. "Fixed Point Theorems in Ordered Banach Spaces and Applications to Nonlinear Integral Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. M. A. Kutbi & Jamshaid Ahmad & Nawab Hussain & Muhammad Arshad, 2013. "Common Fixed Point Results for Mappings with Rational Expressions," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, June.
    6. Mohamed Jleli & Erdal Karapınar & Bessem Samet, 2013. "Best Proximity Points for Generalized -Proximal Contractive Type Mappings," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-10, May.
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    1. N. Hussain & M. A. Kutbi & P. Salimi, 2014. "Fixed Point Theory in α‐Complete Metric Spaces with Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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