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

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.