Address: Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, Serbia
E-mail: marco.s@verat.net
Abstract: In this paper, we analyze multi-dimensional quasi-asymptotically $c$-almost periodic functions and their Stepanov generalizations as well as multi-dimensional Weyl $c$-almost periodic type functions. We also analyze several important subclasses of the class of multi-dimensional quasi-asymptotically $c$-almost periodic functions and reconsider the notion of semi-$c$-periodicity in the multi-dimensional setting, working in the general framework of Lebesgue spaces with variable exponent. We provide certain applications of our results to the abstract Volterra integro-differential equations in Banach spaces.
AMSclassification: primary 42A75; secondary 43A60, 47D99.
Keywords: quasi-asymptotically c-almost periodic type functions, (S,{\mathbb{D}})-asymptotically (\omega ,c)-periodic type functions, S-asymptotically (\omega _{j},c_{j},{\mathbb{D}}_{j})_{j\in {\mathbb{N}}_{n}}-periodic type functions, semi-(c_{j})_{j\in {\mathbb{N}}_{n}}-periodic type functions, Weyl c-almost periodic type functions, abstract Volterra integro-differential equations.
DOI: 10.5817/AM2021-4-221