ASYMPTOTIC EQUIVALENCE AND KOBAYASHI-TYPE ESTIMATES FOR NONAUTONOMOUS MONOTONE OPERATORS IN BANACH SPACES

We provide a sharp generalization to the nonautonomous case of the well-known Kobayashi estimate for proximal iterates associated with maximal monotone operators. We then derive a bound for the distance between a continuous-in-time trajectory, namely the solution to the differential inclusion. (x)over dot + A(t)x there exists 0, and the corresponding proximal iterations. We also establish continuity properties with respect to time of the nonautonomous flow under simple assumptions by revealing their link with the function t bar right arrow A(t). Moreover, our sharper estimations allow us to derive equivalence results which are useful to compare the asymptotic behavior of the trajectories defined by different evolution systems. We do so by extending a classical result of Passty to the nonautonomous setting.