On Stepanov-like almost periodicity in mixed Lebesgue spaces

The main purpose of this paper is to revisit the recently analyzed class of multi-dimensional Stepanov almost periodic functions. We introduce and study several new classes of Stepanov-like almost periodic functions in the mixed Lebesgue spaces. We also provide a new application of multi-dimensional Stepanov almost periodic functions to the abstract nonautonomous differential equations of first order, provided that all components of the exponent $\vec{p}\in [1,\infty)^{n}$ are equal.