Публикации автора

The main purpose of this paper is to revisit the recently analyzed class of multidimensional 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 p_ ∈ [1, ∞)n are equal.

We analyze the metrical Bochner criterion and a new class of multi-dimensional metrically Stepanov almost periodic type functions. We clarify the main structural properties for the introduced classes of functions, including the Bochner criterion, and provide certain applications to Doss-p-almost periodic functions. We also study the extensions of almost periodic sequences and briefly explain how we can apply the established theoretical results to the abstract Volterra integro-differential equation

We consider several new classes of metrically ρ-almost periodic type functions F: I ×X →Y, where ∅ = I ⊆ Rn, X is an arbitrary non-empty set and Y is a sequentially completelocally convex space. We briefly explain how the introduced notion can be useful in the study of qualitative analysis of solutions for some classes of the abstract Volterra integro-differential inclusions in locally convex spaces.