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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.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:219695
DOI: 10.1155/2014/219695
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