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Fixed point theorems and weak convergence theorems for generalized hybrid mappings in Hilbert spaces. (English) Zbl 1226.47053
Summary: We first consider a broad class of nonlinear mappings containing the classes of nonexpansive mappings, nonspreading mappings, and hybrid mappings in a Hilbert space. Then, we deal with fixed point theorems and weak convergence theorems for these nonlinear mappings in a Hilbert space.

MSC:
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
47H05 Monotone operators and generalizations
47H25 Nonlinear ergodic theorems
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