Cauchy’s functional equation and extensions: Goldie’s equation and inequality, the Gołąb–Schinzel equation and Beurling’s equation

Abstract

The Cauchy functional equation is not only the most important single functional equation, it is also central to regular variation. Classical Karamata regular variation involves a functional equation and inequality due to Goldie; we study this, and its counterpart in Beurling regular variation, together with the related Gołąb–Schinzel equation