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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:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems

Citations:

Zbl 1035.47048
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References:

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