Some improvements on weak convergence theorems of Chuang and Takahashi in Hilbert spaces
Keywords:
fixed point, k-demicontractive mapping, Mann iteration, Ishikawa iteration, extragradient methodAbstract
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 -demicontractive mappings where
. Obviously, the class of
-demicontractive mappings contains all firmly nonexpansive mappings. The situation
is extensively studied by means of the Ishikawa iteration and the extragradient method of Korpelevi
. Some numerical results for
are presented and further discussed.