Weak Convergence Theorems of Three Iterative Methods for Strictly Pseudocontractive Mappings of Browder-Petryshyn Type

Let Open image in new window be a real Open image in new window -uniformly smooth Banach space which is also uniformly convex (e.g., Open image in new window or Open image in new window spaces Open image in new window , and Open image in new window a nonempty closed convex subset of Open image in new window . By constructing nonexpansive mappings, we elicit the weak convergence of Mann's algorithm for a Open image in new window -strictly pseudocontractive mapping of Browder-Petryshyn type on Open image in new window in condition thet the control sequence Open image in new window is chosen so that (i) Open image in new window (ii) Open image in new window , where Open image in new window . Moreover, we consider to find a common fixed point of a finite family of strictly pseudocontractive mappings and consider the parallel and cyclic algorithms for solving this problem. We will prove the weak convergence of these algorithms.