We prove some stability and hyperstability results for a generalization of the well known Fréchet functional equation, stemming from one of the characterizations of the inner product spaces. As the main tool we use a fixed point theorem for some function spaces. We end the paper with some new inequalities characterizing the inner product spaces.
@article{bwmeta1.element.doi-10_1515_aupcsm-2015-0006,
author = {Renata Malejki},
title = {Stability of a generalization of the Fr\'echet functional equation},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
volume = {14},
year = {2015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_aupcsm-2015-0006}
}
Renata Malejki. Stability of a generalization of the Fréchet functional equation. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 14 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_aupcsm-2015-0006/