On slowly varying sequences

Abstract

In this paper we investigate the connection between the class SV s of slowly varying sequences (in the sense of Karamata) and the slow equivalence, strong asymptotic equivalence, selection principles and game theory.

On Rapid Equivalence and Translational Rapid Equivalence

“…Motivated by the study of some equivalence relations on classes of functions and sequences given in [7,8,14], in this paper we define a relation on the class of translationally rapidly varying sequences and investigate some properties of this relation. In particular, we study relationships of this relation with selection principles and game theory complementing the research in [2,3,5,6].…”

“…for each λ > 1. We denote it by c r ∼ d as n → +∞ (see, e.g., [8,14]). Let c be a nondecreasing sequence from a subset V of S. The capacity of c with respect to V is the subfamily of S given by M…”

Logarithmic (translationally) rapidly varying sequences and selection principles

“…Kočinac's selection principles α i (A, B), i ∈ {2, 3, 4} (see e.g. [18]) are very important in selection principles theory. Evidently, α 2 (A, B) =⇒ α 3 (A, B) =⇒ α 4 (A, B).…”