Approximation Theorems for Exponentially Bounded <i>a</i>-Times Integrated Cosine Function

Abstract

In this paper, based on the theories of α-times Integrated Cosine Function, we discuss the approximation theorem for α -times Integrated Cosine Function and conclude the approximation theorem of exponentially bounded α -times Integrated Cosine Function by the approximation theorem of n -times integrated semigroups. If the semigroups are equicontinuous at each point , we give different methods to prove the theorem.