First a stability result of Prager-Schwaiger [Prager W., Schwaiger J., Stability of the multi-Jensen equation, Bull. Korean Math. Soc., 2008, 45(1), 133–142] is generalized by admitting more general domains of the involved function and by allowing the bound to be not constant. Next a result by Cieplinski [Cieplinski K., On multi-Jensen functions and Jensen difference, Bull. Korean Math. Soc., 2008, 45(4), 729–737] is discussed. Finally a characterization of the completeness of a normed space in terms of stability requirements for multi-Jensen functions is presented.
@article{bwmeta1.element.doi-10_2478_s11533-013-0215-y,
author = {Jens Schwaiger},
title = {Some remarks on the stability of the multi-Jensen equation},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {966-971},
zbl = {1273.39026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0215-y}
}
Jens Schwaiger. Some remarks on the stability of the multi-Jensen equation. Open Mathematics, Tome 11 (2013) pp. 966-971. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0215-y/
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