Remotely $c$-almost periodic type functions in ${\mathbb{R}}^n$

Abstract

In this paper, we relate the notions of remote almost periodicity and quasi-asymptotical almost periodicity; in actual fact, we observe that a remotely almost periodic function is nothing else but a bounded, uniformly continuous quasi-asymptotically almost periodic function. We introduce and analyze several new classes of remotely $c$-almost periodic functions in ${\mathbb{R}}^n,$ slowly oscillating functions in ${\mathbb{R}}^n,$ and further analyze the recently introduced class of quasi-asymptotically $c$-almost periodic functions in ${\mathbb{R}}^n.$ We provide certain applications of our theoretical results to the abstract Volterra integro-differential equations and the ordinary differential equations.