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

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  • 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, Hindawi, vol. 2014, pages 1-7, August.
    • Handle: RePEc:hin:jnlaaa:219695
    DOI: 10.1155/2014/219695
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