Abstract :
Let X be a complex Banach space, and let tªT t. 5T t.5F1, tG0. be a
strongly continuous contraction semigroup on X.with infinitesimal generator A.
This paper proves that
1024 104
5Ax54F 5x535A4x5, 5A2x54F 5x525A4x52,
3 9
5 A3x5 4F1925x5 5A4x53
hold for every xgD A4.. Inequalities are established also for uniformly bounded
strongly continuous semigroups, groups, and cosine functions
