DOI: 10.3390/axioms13030189 ISSN: 2075-1680

Translational Regular Variability and the Index Function

Danica Fatić, Dragan Djurčić, Ljubiša D. R. Kočinac
  • Geometry and Topology
  • Logic
  • Mathematical Physics
  • Algebra and Number Theory
  • Analysis

This paper deals with translational regular and rapid variations. By using a new method of proving the Galambos–Bojanić-Seneta type theorems, we prove two theorems of this type for translationally regularly varying and translationally rapidly varying functions and sequences, important objects in the asymptotic analysis of divergent processes. Also, we introduce and study the index functions for translationally regularly varying functions and sequences. For example, we prove that the index function of a translationally regularly varying function is also in the same class of functions.

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