Metrical Approximations of Functions

Abstract

In this paper, we analyze metrical approximations of functions F : Λ × X → Y by trigonometric polynomials and ρ-periodic type functions, where ∅ ≠ Λ ⊆ Rⁿ, X and Y are complex Banach spaces, and ρ is a general binary relation on Y. Besides the classical concept, we analyze Stepanov, Weyl, Besicovitch and Doss generalized approaches to metrical approximations. We clarify many structural properties of introduced spaces of functions and provide some illustrative applications to the abstract PDEs.