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

Abstract

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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Correspondence to Ying Zhang.

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Zhang, Y., Guo, Y. Weak Convergence Theorems of Three Iterative Methods for Strictly Pseudocontractive Mappings of Browder-Petryshyn Type. Fixed Point Theory Appl 2008, 672301 (2008). https://doi.org/10.1155/2008/672301

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  • DOI: https://doi.org/10.1155/2008/672301

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