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Zbl 1217.47128
Takahashi, Wataru; Yao, Jen-Chih; Kocourek, Pavel
Weak and strong convergence theorems for generalized hybrid nonself-mappings in Hilbert spaces. (English)
[J] J. Nonlinear Convex Anal. 11, No. 3, 567-586 (2010). ISSN 1345-4773; ISSN 1880-5221/e

The authors obtain fundamental results for a broad class of nonlinear maps containing the classes of nonexpansive maps, nonspreading maps and hybrid maps in a Hilbert space. They prove weak convergence theorems of Mann's type for super hybrid maps in a Hilbert space. They further obtain strong convergence theorems for the super hybrid maps introduced by {\it K. Nakajo} and {\it W. Takahashi} [J. Math. Anal. Appl. 279, No. 2, 372--379 (2003; Zbl 1035.47048)] and {\it W. Takahashi, Y. Takeuchi} and {\it R. Kubota} [J. Math. Anal. Appl. 341, No. 1, 276--286 (2008; Zbl 1134.47052)].
[Edward Prempeh (Kumasi)]

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47H09 Mappings defined by "shrinking" properties
47H05 Monotone operators (with respect to duality)

Keywords: Hilbert space; nonexpansive mapping; nonspreading mapping; hybrid mapping; fixed point; weak convergence; hybrid method

Citations: Zbl 1035.47048; Zbl 1134.47052

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