Fixed point theorems for one-parameter asymptotically nonexpansive semigroups in general Banach spaces

In this paper, we first prove two fixed points theorems for one-parameter asymptotically nonexpansive semigroups in general Banach spaces. Using these results, we prove a strong convergence theorem of Mann's type sequences for the asymptotically nonexpansive semigroups. This is a generalization of the result of Suzuki and Takahashi for one-parameter nonexpansive semigroups in general Banach spaces.