ATTRACTIVE POINT AND WEAK CONVERGENCE THEOREMS FOR NEW GENERALIZED HYBRID MAPPINGS IN HILBERT SPACES

In this paper we introduce a broad class of nonlinear mappings which contains the class of contractive mappings and the class of generalized hybrid mappings in a Hilbert space. Then we prove an attractive point theorem for such mappings in a Hilbert space. Furthermore, we prove a mean convergence theorem of Baillon's type without convexity in a Hilbert space. Finally, we prove a weak convergence theorem of Mann's type [12] without closedness. These results generalize attractive point, mean convergence and weak convergence theorems proved by Takahashi and Takeuchi [18], and Kocourek, Takahashi and Yao [8].