Asymptotic Behavior of Solutions of Nonlinear Volterra Equations and Mean Points1

In this paper, we study the asymptotic behavior of solutions to a nonlinear Volterra equation in Banach spaces. First, we deal with the mean point concerning an invariant mean on Ž0, . for the ‘‘unbounded behavior’’ of solutions in a reflexive Banach space. Using the mean point, we obtain the weak and strong convergences for the ‘‘unbounded behavior’’ of solutions in a reflexive and strictly convex Banach space and in the dual space which has a Fr´echet differentiable norm, respectively.