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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
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
Summary:
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.
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