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Monotone CQ iteration processes for nonexpansive semigroups and maximal monotone operators. (English) Zbl 1220.47122
Summary: K. Nakajo and 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 K. Nakajo and 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:
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47H10Fixed point theorems for nonlinear operators on topological linear spaces