Measure ω , c

Abstract

The primary aim of this work is to introduce a new class of functions called $\mu$ - $\left(\omega ,c\right)$ -pseudo-almost periodic functions. Using the measure theory, we generalize in a natural way some recent works and study some properties of those $\mu$ - $\left(\omega ,c\right)$ -pseudo-almost periodic functions including two new composition results which play a crucial role for the existence of some $\mu$ - $\left(\omega ,c\right)$ -pseudo-almost periodic solutions of certain semilinear differential equations and partial differential equations. We also investigate the existence and uniqueness of the $\mu$ - $\left(\omega ,c\right)$ -pseudo-almost periodic solutions for some models of Lasota-Wazewska equation with measure $\left(\omega ,c\right)$ -pseudo-almost periodic coefficient and mixed delays.