The problem of invariance of the geometric mean in the class of Lagrangian means was considered in [Głazowska D., Matkowski J., An invariance of geometric mean with respect to Lagrangian means, J. Math. Anal. Appl., 2007, 331(2), 1187–1199], where some necessary conditions for the generators of Lagrangian means have been established. The question if all necessary conditions are also sufficient remained open. In this paper we solve this problem.
@article{bwmeta1.element.doi-10_2478_s11533-011-0059-2,
author = {Dorota G\l azowska},
title = {A solution of an open problem concerning Lagrangian mean-type mappings},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {1067-1073},
zbl = {1232.26052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0059-2}
}
Dorota Głazowska. A solution of an open problem concerning Lagrangian mean-type mappings. Open Mathematics, Tome 9 (2011) pp. 1067-1073. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0059-2/
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