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New Results and Generalizations for Approximate Fixed Point Property and Their Applications

Author

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  • Wei-Shih Du
  • Farshid Khojasteh

Abstract

We first introduce the concept of manageable functions and then prove some new existence theorems related to approximate fixed point property for manageable functions and α‐admissible multivalued maps. As applications of our results, some new fixed point theorems which generalize and improve Du′s fixed point theorem, Berinde‐Berinde′s fixed point theorem, Mizoguchi‐Takahashi′s fixed point theorem, and Nadler′s fixed point theorem and some well‐known results in the literature are given.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:581267
    DOI: 10.1155/2014/581267
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    References listed on IDEAS

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    1. 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).
    2. Wei-Shih Du, 2012. "On Approximate Coincidence Point Properties and Their Applications to Fixed Point Theory," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, May.
    3. 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).
    4. 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).
    5. Wei-Shih Du, 2013. "On Caristi Type Maps and Generalized Distances with Applications," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, September.
    6. Wei-Shih Du, 2013. "On Caristi Type Maps and Generalized Distances with Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    7. 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).
    8. Wei-Shih Du, 2013. "New Existence Results and Generalizations for Coincidence Points and Fixed Points without Global Completeness," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, February.
    9. 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.
    10. Wei-Shih Du & Erdal Karapınar & Naseer Shahzad, 2013. "The Study of Fixed Point Theory for Various Multivalued Non-Self-Maps," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, August.
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    Cited by:

    1. Abdul Latif & Dinh The Luc, 2014. "A General Fixed Point Theorem for Multivalued Mappings That Are Not Necessarily Contractions and Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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