A Landau-Kolmogorov type inequality for generators of a class of strongly continuous families of bounded linear operators on Banach space is investigated. In particular, the authors establish a Landau-Kolmogorov inequality when is a generator of certain regularized resolvents defined on a Banach space . Specifically, they show that, if is a pair satisfying the -condition and
and if is a generator of an -regularized resolvent such that , , with , then the Landau-Kolmogorov inequality
holds for all , where and are positive functions. Examples are given to illustrate the obtained results.