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A Fixed Point Theorem for Multivalued Mappings with δ‐Distance

Author

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  • Özlem Acar
  • Ishak Altun

Abstract

We mainly study fixed point theorem for multivalued mappings with δ‐distance using Wardowski’s technique on complete metric space. Let (X, d) be a metric space and let B(X) be a family of all nonempty bounded subsets of X. Define δ:B(X)×B(X)→R by δ(A, B) = sup{d(a, b) : a ∈ A, b ∈ B}. Considering δ‐distance, it is proved that if (X, d) is a complete metric space and T : X → B(X) is a multivalued certain contraction, then T has a fixed point.

Suggested Citation

  • Özlem Acar & Ishak Altun, 2014. "A Fixed Point Theorem for Multivalued Mappings with δ‐Distance," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:497092
    DOI: 10.1155/2014/497092
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    References listed on IDEAS

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    1. Marwan Amin Kutbi & Wutiphol Sintunavarat, 2013. "The Existence of Fixed Point Theorems via w‐Distance and α‐Admissible Mappings and Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Marwan Amin Kutbi & Wutiphol Sintunavarat, 2013. "The Existence of Fixed Point Theorems via -Distance and -Admissible Mappings and Applications," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, October.
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