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Zbl 1220.47122
Su, Yongfu; Qin, Xiaolong
(Su, Yong-fu; Qin, Xiao-long)
Monotone CQ iteration processes for nonexpansive semigroups and maximal monotone operators. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 68, No. 12, A, 3657-3664 (2008). ISSN 0362-546X

Summary: {\it K. Nakajo} and {\it W. Takahashi} [J. Math. Anal. Appl. 279, No.~2, 372--379 (2003; Zbl 1035.47048)] proved strong convergence theorems for nonexpansive mappings, nonexpansive semigroups and the proximal point algorithm for zero-points of monotone operators in Hilbert spaces by the CQ iteration method. The purpose of this paper is to modify the CQ iteration method of {\it K. Nakajo} and {\it W. Takahashi} [loc.\,cit.]\ using the monotone CQ method, and to prove strong convergence theorems. The Cauchy sequence method is used, so we proceed without use of the demiclosedness principle and Opial's condition, and other weak topological techniques.

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: strong convergence; CQ method; nonexpansive mapping; nonexpansive semigroup; proximal point algorithm

Citations: Zbl 1035.47048

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