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Strong Convergence of a Unified General Iteration for k‐Strictly Pseudononspreading Mapping in Hilbert Spaces

Author

Listed:
  • Dao-Jun Wen
  • Yi-An Chen
  • Yan Tang

Abstract

We introduce a unified general iterative method to approximate a fixed point of k‐strictly pseudononspreading mapping. Under some suitable conditions, we prove that the iterative sequence generated by the proposed method converges strongly to a fixed point of a k‐strictly pseudononspreading mapping with an idea of mean convergence, which also solves a class of variational inequalities as an optimality condition for a minimization problem. The results presented in this paper may be viewed as a refinement and as important generalizations of the previously known results announced by many other authors.

Suggested Citation

  • Dao-Jun Wen & Yi-An Chen & Yan Tang, 2014. "Strong Convergence of a Unified General Iteration for k‐Strictly Pseudononspreading Mapping in Hilbert Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:219695
    DOI: 10.1155/2014/219695
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    References listed on IDEAS

    as
    1. Dao-Jun Wen, 2011. "Strong Convergence Theorems for Equilibrium Problems and k‐Strict Pseudocontractions in Hilbert Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    2. L. C. Ceng & A. Petruşel & J. C. Yao, 2009. "Iterative Approaches to Solving Equilibrium Problems and Fixed Point Problems of Infinitely Many Nonexpansive Mappings," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 37-58, October.
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