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Best Proximity Points for Generalized Proximal Weak Contractions Satisfying Rational Expression on Ordered Metric Spaces

Author

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  • V. Pragadeeswarar
  • M. Marudai

Abstract

We introduce a generalized proximal weak contraction of rational type for the non‐self‐map and proved results to ensure the existence and uniqueness of best proximity point for such mappings in the setting of partially ordered metric spaces. Further, our results provides an extension of a result due to Luong and Thuan (2011) and also it provides an extension of Harjani (2010) to the case of self‐mappings.

Suggested Citation

  • V. Pragadeeswarar & M. Marudai, 2015. "Best Proximity Points for Generalized Proximal Weak Contractions Satisfying Rational Expression on Ordered Metric Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:361657
    DOI: 10.1155/2015/361657
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    References listed on IDEAS

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    1. J. Harjani & B. López & K. Sadarangani, 2010. "A Fixed Point Theorem for Mappings Satisfying a Contractive Condition of Rational Type on a Partially Ordered Metric Space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    2. Erdal Karapınar & V. Pragadeeswarar & M. Marudai, 2014. "Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. Erdal Karapınar & V. Pragadeeswarar & M. Marudai, 2014. "Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-6, January.
    4. 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.
    5. 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).
    6. J. Harjani & B. López & K. Sadarangani, 2010. "A Fixed Point Theorem for Mappings Satisfying a Contractive Condition of Rational Type on a Partially Ordered Metric Space," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-8, September.
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