We introduce the notion of regularized quasi-semigroupof bounded linear operators on Banach spaces and its infinitesimal generator, as a generalization of regularized semigroups ofoperators. 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.
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