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On Approximate Coincidence Point Properties and Their Applications to Fixed Point Theory

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  • Wei-Shih Du

Abstract

We first establish some existence results concerning approximate coincidence point properties and approximate fixed point properties for various types of nonlinear contractive maps in the setting of cone metric spaces and general metric spaces. From these results, we present some new coincidence point and fixed point theorems which generalize Berinde‐Berinde′s fixed point theorem, Mizoguchi‐Takahashi′s fixed point theorem, and some well‐known results in the literature.

Suggested Citation

  • Wei-Shih Du, 2012. "On Approximate Coincidence Point Properties and Their Applications to Fixed Point Theory," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:302830
    DOI: 10.1155/2012/302830
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    References listed on IDEAS

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    1. Wei-Shih Du, 2011. "The Existence of Cone Critical Point and Common Fixed Point with Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    2. Wei-Shih Du, 2011. "The Existence of Cone Critical Point and Common Fixed Point with Applications," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-22, October.
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    Cited by:

    1. Yi-Chou Chen, 2013. "Infinitely Many Quasi‐Coincidence Point Solutions of Multivariate Polynomial Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Wei-Shih Du & Erdal Karapınar & Naseer Shahzad, 2013. "The Study of Fixed Point Theory for Various Multivalued Non‐Self‐Maps," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Wei-Shih Du, 2013. "New Existence Results and Generalizations for Coincidence Points and Fixed Points without Global Completeness," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Wei-Shih Du & Farshid Khojasteh, 2014. "New Results and Generalizations for Approximate Fixed Point Property and Their Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Wei-Shih Du, 2013. "On Caristi Type Maps and Generalized Distances with Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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