## 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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