WEAK AND STRONG MEAN CONVERGENCE THEOREMS FOR SUPER HYBRID MAPPINGS IN HILBERT SPACES
Mayumi Hojo, Wataru Takahashi, Jen‐Chih Yao · 2011
In this paper, we first introduce a class of nonlinear mappings called extended hybrid in a Hilbert space containing the class of generalized hybrid mappings. The class is dierent from the class of super hybrid mappings which was defined by Kocourek, Takahashi and Yao (12). We prove a fixed point theorem for generalized hybrid nonself-mapping in a Hilbert space. Next, we prove a nonlinear ergodic theorem of Baillon's type for super hybrid mappings in a Hilbert space. Finally, we deal with two strong convergence theorems of Halpern's type for these nonlinear mappings in a Hilbert space.