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Keywords:
remotely $c$-almost periodic functions in ${\mathbb{R}}^{n}$; slowly oscillating functions in ${\mathbb{R}}^{n}$; quasi-asymptotically $c$-almost periodic functions in ${\mathbb{R}}^{n}$; abstract Volterra integro-differential equations; Richard-Chapman ordinary differential equation with external perturbation
remotely $c$-almost periodic functions in ${\mathbb{R}}^{n}$; slowly oscillating functions in ${\mathbb{R}}^{n}$; quasi-asymptotically $c$-almost periodic functions in ${\mathbb{R}}^{n}$; abstract Volterra integro-differential equations; Richard-Chapman ordinary differential equation with external perturbation
Summary:
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.
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