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

Abstract

The purpose of this paper is to introduce and construct the implicit and explicit viscosity iterative processes by a generalized contraction mapping f and a nonexpansive semigroup { 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 } in reflexive Banach spaces which admits a weakly sequentially continuous duality mapping.