Asymptotically almost periodic type functions of several variables and applications

Abstract

In this paper, we introduce and analyze several new classes of ${\mathbb D}$-asymptotically almost periodic type functions of the form $F : I\times X \rightarrow Y,$ where $\emptyset \neq I \subseteq {\mathbb R}^{n}$, $(X,\| \cdot \|)$ and $(Y,\| \cdot \|_{Y})$ are complex Banach spaces. We present many structural results for the introduced classes of ${\mathbb D}$-asymptotically almost periodic type functions, providing also some illustrative examples and applications of the established results to the abstract Volterra integro-differential equations.