We introduce the notion of regularized quasi-semigroup of bounded linear operators on Banach spaces and its infinitesimal generator, as a generalization of regularized semigroups of operators. After some examples of such quasi-semigroups, the properties of this family of operators will be studied. Also some applications of regularized quasi-semigroups in the abstract evolution equations will be considered. Next some elementary perturbation results on regularized quasi-semigroups will be discussed.
"On Regularized Quasi-Semigroups and Evolution Equations." Abstr. Appl. Anal. 2010 1 - 13, 2010. https://doi.org/10.1155/2010/785428