EXISTENCE AND MEAN APPROXIMATION OF FIXED POINTS OF GENERALIZED HYBRID MAPPINGS IN HILBERT SPACES

In this paper, we introduce a broad class of nonlinear mappings in a Hilbert space which covers the class of super generalized hybrid mappings and the class of widely generalized hybrid mappings defined by Kocourek, Takahashi and Yao [11] and the authors [10], respectively. Then we prove fixed point theorems for such new mappings. Furthermore, we prove nonlinear ergodic theorems of Baillon's type in a Hilbert space. It seems that the results are new and useful. For example, using our fixed point theorems, we can directly prove Browder and Petryshyn's fixed point theorem [5] for strict pseudo-contractive mappings and Kocourek, Takahashi and Yao's fixed point theorem [11] for super generalized hybrid mappings.