Remarks on Different Approaches to the Theory of Higher-Order Types of Asymptotic Variation

Abstract

As a completion of the previously published theory of higher-order types of asymptotic variation, we point out some remarks about different approaches to construct such an advanced and demanding theory, because there are various (non-equivalent) approaches to the basic concepts of types of asymptotic variation, i . e ., the concepts not involving derivatives. After listing the five known approaches to the concept of regular variation and their mutual relationships, we show that, as far as the higher-order theory is concerned, there is essentially “ only one way ” to construct such a theory for differentiable functions.