Viscosity approximation methods for a nonexpansive semigroup in Banach spaces with gauge functions

We first investigate strong convergence of the sequence generated by implicit and explicit viscosity approximation methods for a one-parameter nonexpansive semigroup in a real Banach space E which has a uniformly Gâteaux differentiable norm and admits the duality mapping j <Subscript> φ </Subscript>, where φ is a gauge function on [0, ∞). The main results also improve and extend some known results concerning the normalized duality mapping in the literature. Copyright Springer Science+Business Media, LLC. 2012