WEAK AND STRONG CONVERGENCE THEOREMS FOR WIDELY MORE GENERALIZED HYBRID MAPPINGS IN HILBERT SPACES

In this paper, using strongly asymptotically invariant sequences, we first prove a weak convergence theorem of Mann's type [18] for widely more generalized hybrid mappings in a Hilbert space. Furthermore, using the idea of mean convergence by Shimizu and Takahashi [19, 20], we prove a strong convergence theorem of Halpern's type [6] for widely more generalized hybrid mappings in a Hilbert space. This theorem generalizes Hojo and Takahashi's strong convergence theorem [7] for generalized hybrid mappings.