Address:
Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, Serbia
Max-Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany
E-mail:
marco.s@verat.net
math.vipinkumar219@gmail.com
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.
AMSclassification: primary 42A75; secondary 43A60, 47D99.
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.
DOI: 10.5817/AM2022-2-85