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Nonlinear ergodic theorem without convexity for generalized hybrid mappings in a Hilbert space. (English) Zbl 1230.47085
The authors of the present paper treat the concept of attractive points of a nonlinear mapping in real Hilbert space and obtain some fundamental properties. Based on these results, a mean convergence theorem without convexity for finding an attractive point of a generalized hybrid mapping is proved.

MSC:
47H25Nonlinear ergodic theorems
47H05Monotone operators (with respect to duality) and generalizations
47H09Mappings defined by “shrinking” properties