Regularized semigroups and integrated semigroups are introduced by Da Prato and Arendt respectively, to treat Cauchy problems which are not well posed. deLaubenfels have studied the relationship between these two different semigroups. We give the relations between regularized α times resolvent families and integrated α times resolvent families, which generalizes the corresponding results for regularized semigroups and integrated semigroups given by deLaubenfels. In the end we give some corollaries.
