Some improvements on weak convergence theorems of Chuang and Takahashi in Hilbert spaces

Chuang and Takahashi [3] recently proved three weak convergence theorems for a family of firmly nonexpansive mappings with generalized parameters. We discuss these three results for a family of $k$-demicontractive mappings where $k \le 1$. Obviously, the class of $k$-demicontractive mappings contains all firmly nonexpansive mappings. The situation $k = 1$ is extensively studied by means of the Ishikawa iteration and the extragradient method of Korpelevič. Some numerical results for $k = 1$ are presented and further discussed.