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Weak and strong convergence theorems for generalized hybrid nonself-mappings in Hilbert spaces. (English) Zbl 1217.47128
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 K. Nakajo and W. Takahashi [J. Math. Anal. Appl. 279, No. 2, 372–379 (2003; Zbl 1035.47048)] and W. Takahashi, Y. Takeuchi and R. Kubota [J. Math. Anal. Appl. 341, No. 1, 276–286 (2008; Zbl 1134.47052)].
MSC:
47J25Iterative procedures (nonlinear operator equations)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47H09Mappings defined by “shrinking” properties
47H05Monotone operators (with respect to duality) and generalizations