Viscosity approximation to common fixed points of a nonexpansive semigroup with a generalized contraction mapping

The purpose of this paper is to introduce and construct the implicit and explicit viscosity iterative processes by a generalized contraction mapping ff and a nonexpansive semigroup {T(t):t⩾0}{T(t):t⩾0}, and to prove that under suitable conditions these iterative processes converge strongly to a unique common fixed point of {T(t):t⩾0}{T(t):t⩾0} in reflexive Banach spaces which admits a weakly sequentially continuous duality mapping.