Some remarks on comparison functions
Volume 96 / 2009
Annales Polonici Mathematici 96 (2009), 97-106
MSC: 34A12, 34A40.
DOI: 10.4064/ap96-2-1
Abstract
We answer some questions concerning Perron and Kamke comparison functions satisfying the Carathéodory condition. In particular, we show that a Perron function multiplied by a constant may not be a Perron function, and that not every comparison function is bounded by a comparison function with separated variables. Moreover, we investigate when a sum of Perron functions is a Perron function. We also present a criterion for comparison functions with separated variables.
