Lizama, Carlos; Sánchez, Justino On perturbation of \(K\)-regularized resolvent families. (English) Zbl 1051.45009 Taiwanese J. Math. 7, No. 2, 217-227 (2003). The authors introduce the notion of a \(k\)-regularized resolvent family, being a resolvent family satisfying a given Volterra integral equation, and express the generator of the resolvent family in terms of the kernel function \(k\), specialize the result for \(\alpha\)-integrated semigroup generators, and derive an additive perturbation result. Reviewer: Cornelis van der Mee (Cagliari) Cited in 1 ReviewCited in 31 Documents MSC: 45N05 Abstract integral equations, integral equations in abstract spaces 47D62 Integrated semigroups 45D05 Volterra integral equations Keywords:integrated semigroup; Volterra integral equation; resolvent family; perturbation PDFBibTeX XMLCite \textit{C. Lizama} and \textit{J. Sánchez}, Taiwanese J. Math. 7, No. 2, 217--227 (2003; Zbl 1051.45009) Full Text: DOI