Granata, A. (2016) The Theory of Higher-Order Types of Asymptotic Variation for Differentiable Functions. Part II: Algebraic Operations and Types of Exponential Variation. Advances in Pure Mathematics, 6, 817-867.
https://doi.org/10.4236/apm.2016.612064

has been cited by the following article:

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

  AUTHORS: Antonio Granata

  KEYWORDS: Higher-Order Types of Asymptotic Variation, Hardy’s Approach, Karamata’s Approach, Bourbaki-Dieudonné’s Approach, Zygmund’s Approach

  JOURNAL NAME: Advances in Pure Mathematics, Vol.16 No.1, January 27, 2026

  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.