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Convergence Theorems for Fixed Points of Multivalued Strictly Pseudocontractive Mappings in Hilbert Spaces

Author

Listed:
  • C. E. Chidume
  • C. O. Chidume
  • N. Djitté
  • M. S. Minjibir

Abstract

Let K be a nonempty, closed, and convex subset of a real Hilbert space H. Suppose that T : K → 2K is a multivalued strictly pseudocontractive mapping such that F(T) ≠ ∅. A Krasnoselskii‐type iteration sequence {xn} is constructed and shown to be an approximate fixed point sequence of T; that is, limn→∞d(xn, Txn) = 0 holds. Convergence theorems are also proved under appropriate additional conditions.

Suggested Citation

  • C. E. Chidume & C. O. Chidume & N. Djitté & M. S. Minjibir, 2013. "Convergence Theorems for Fixed Points of Multivalued Strictly Pseudocontractive Mappings in Hilbert Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:629468
    DOI: 10.1155/2013/629468
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    References listed on IDEAS

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    1. John Geanakoplos, 2003. "Nash and Walras equilibrium via Brouwer," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 585-603, March.
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    Cited by:

    1. F. O. Isiogugu, 2016. "Approximation of a Common Element of the Fixed Point Sets of Multivalued Strictly Pseudocontractive‐Type Mappings and the Set of Solutions of an Equilibrium Problem in Hilbert Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2016(1).
    2. C. E. Chidume & A. U. Bello & P. Ndambomve, 2014. "Strong and Δ‐Convergence Theorems for Common Fixed Points of a Finite Family of Multivalued Demicontractive Mappings in CAT(0) Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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