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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap96-2-1,
author = {Antoni Augustynowicz},
title = {Some remarks on comparison functions},
journal = {Annales Polonici Mathematici},
volume = {95},
year = {2009},
pages = {97-106},
zbl = {1175.34005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap96-2-1}
}
Antoni Augustynowicz. Some remarks on comparison functions. Annales Polonici Mathematici, Tome 95 (2009) pp. 97-106. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap96-2-1/