STEPANOV AND WEYL CLASSES OF MULTI-DIMENSIONAL Ρ-Almost PERIODIC TYPE FUNCTIONS M. KOSTIC

Abstract

In this paper, we analyze Stepanov and Weyl classes of multidimensional ρ-almost periodic type functions F : I × X → Y , where n ∈ N, ∅ = I ⊆ R n , X and Y are complex Banach spaces and ρ is a binary relation on Y, working in the general setting of Lebesgue spaces with variable exponents. We provide the main structural characterizations for the introduced classes of functions and apply our results to the abstract Volterra integro-differential equations.2010 Mathematics Subject Classification. 42A75, 43A60, 47D99. Key words and phrases. Stepanov multi-dimensional ρ-almost periodic type functions, Weyl multi-dimensional ρ-almost periodic type functions, abstract Volterra integro-differential equations.