In this talk, we discuss the existence of computable rates of asymptotic regularity for Ces`aro means for mappings with a modulus of regularity in a general setting. We also examine the computable rates of convergence of Ces`aro means as well as the vector valued integrals with respect to means on semigroups. Additionally, we investigate the existence and uniqueness of solutions to a general second order differential inclusion of accretive type, which is new in Banach spaces. Furthermore, for the semigroup generated by these solutions, we present a quantitative result in the form of a rate of convergence that depends, among other elements, on a modulus for the convergence condition.
