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

Abstract. In this paper, we analyze multi-dimensional quasi-asymptotically c-almost periodic functions and their Stepanov generalizations as well as multidimensional Weyl c-almost periodic type functions. We also analyze several important subclasses of the class of multi-dimensional quasi-asymptotically calmost 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.