A general iterative algorithm for semigroups of nonexpansive mappings with generalized contractive mapping

The purpose of this paper is to study the strong convergence of the implicit and composite viscosity iteration schemes to a unique common fixed point of nonexpansive semigroups T, which is a solution of some variational inequality under certain conditions. As a application, we apply the proposed iterative algorithm to the minimization problem of finding a optimality condition. The results of this paper extend some recent results.