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The Generalized Weaker (α‐ϕ‐φ)‐Contractive Mappings and Related Fixed Point Results in Complete Generalized Metric Spaces

Author

Listed:
  • Maryam A. Alghamdi
  • Chi-Ming Chen
  • Erdal Karapınar

Abstract

We introduce the notion of generalized weaker (α‐ϕ‐φ)‐contractive mappings in the context of generalized metric space. We investigate the existence and uniqueness of fixed point of such mappings. Some consequences on existing fixed point theorems are also derived. The presented results generalize, unify, and improve several results in the literature.

Suggested Citation

  • Maryam A. Alghamdi & Chi-Ming Chen & Erdal Karapınar, 2014. "The Generalized Weaker (α‐ϕ‐φ)‐Contractive Mappings and Related Fixed Point Results in Complete Generalized Metric Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:985080
    DOI: 10.1155/2014/985080
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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. Erdal Karapınar & Bessem Samet, 2012. "Generalized α‐ψ Contractive Type Mappings and Related Fixed Point Theorems with Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Chi-Ming Chen & W. Y. Sun, 2012. "Periodic Points and Fixed Points for the Weaker (ϕ, φ)‐Contractive Mappings in Complete Generalized Metric Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. Chi-Ming Chen & W. Y. Sun, 2012. "Periodic Points and Fixed Points for the Weaker ( 𠜙 , 𠜑 ) -Contractive Mappings in Complete Generalized Metric Spaces," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-7, February.
    5. 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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