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

Kostić, M.

Archivum mathematicum, Tome 57 (2021) no. 4, pp. 221-253

Abstract (VO)

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.

Détail

DOI : 10.5817/AM2021-4-221

Classification : 42A75, 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

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