Cyclic Iterative Method for Strictly Pseudononspreading in Hilbert Space

Abstract

Let $\{T_i{\}}_{i=1}^N$ be $N$ strictly pseudononspreading mappings defined on closed convex subset $C$ of a real Hilbert space $H$. Consider the problem of finding a common fixed point of these mappings and introduce cyclic algorithms based on general viscosity iteration method for solving this problem. We will prove the strong convergence of these cyclic algorithm. Moreover, the common fixed point is the solution of the variational inequality $\langle (\gamma f-\mu B)x^{*},v-x^{*}\rangle \le 0,\forall v\in {\bigcap }_{i=1}^N{F}_{ix}(T_i)$.