Metrically $\rho$-almost periodic type functions with values in locally convex spaces

We consider several new classes of metrically $\rho$-almost periodic type functions $F : I \times X \rightarrow Y$, where $\emptyset \neq I \subseteq {\mathbb R}^{n}$, $X$ is an arbitrary non-empty set and $Y$ is a sequentially complete locally convex space. We briefly explain how the introduced notion can be useful in the study of qualitative analysis of solutions for some classes of the abstract Volterra integro-differential inclusions in locally convex spaces.