Weak Convergence Theorems of Three Iterative Methods for Strictly Pseudocontractive Mappings of Browder-Petryshyn Type
Ying Zhang, Yan Guo · Fixed Point Theory and Applications · 2008
Abstract Let "Equation missing" be a real "Equation missing"-uniformly smooth Banach space which is also uniformly convex (e.g., "Equation missing" or "Equation missing" spaces "Equation missing", and "Equation missing" a nonempty closed convex subset of "Equation missing". By constructing nonexpansive mappings, we elicit the weak convergence of Mann's algorithm for a "Equation missing"-strictly pseudocontractive mapping of Browder-Petryshyn type on "Equation missing" in condition thet the control sequence "Equation missing" is chosen so that (i) "Equation missing" (ii) "Equation missing", where "Equation missing". 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.