WEAK AND STRONG CONVERGENCE THEOREMS FOR NONEXPANSIVE SEMIGROUPS IN A BANACH SPACE SATISFYING OPIAL’S CONDITION

Abstract

In this paper, we study the weak convergence of Mann’s type iteration procedure and the existence of nonexpansive retractions for commutative semigroups in Banach spaces which satisfy Opial’s condition. Further, we introduce an implicit iteration procedure for nonexpansive semigroups and then prove a strong convergence theorem for the nonexpansive semigroups in general Banach spaces.