Strong convergence of a unified general iteration for \(k\)-strictly pseudononspreading mapping in Hilbert spaces (Q1722374)

Summary: 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.