Weak Convergence Theorems of Three Iterative Methods for Strictly Pseudocontractive Mappings of Browder-Petryshyn Type
© Y. Zhang and Y. Guo. 2008
Received: 25 September 2007
Accepted: 28 February 2008
Published: 13 March 2008
Let be a real -uniformly smooth Banach space which is also uniformly convex (e.g., or spaces , and a nonempty closed convex subset of . By constructing nonexpansive mappings, we elicit the weak convergence of Mann's algorithm for a -strictly pseudocontractive mapping of Browder-Petryshyn type on in condition thet the control sequence is chosen so that (i) (ii) , where . 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.
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