Abstract and Applied Analysis
Volume 2010 (2010), Article ID 785428, 13 pages
doi:10.1155/2010/785428
Research Article

On Regularized Quasi-Semigroups and Evolution Equations

M. Janfada

Department of Mathematics, Sabzevar Tarbiat Moallem University, P.O. Box 397, Sabzevar, Iran

Received 26 November 2009; Accepted 16 April 2010

Academic Editor: Wolfgang Ruess

Copyright © 2010 M. Janfada. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.