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A solution of an open problem concerning Lagrangian mean-type mappings

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Central European Journal of Mathematics

Abstract

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.

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Authors and Affiliations

  1. Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, Zielona Góra, 65-516, Poland

    Dorota Głazowska

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  1. Dorota Głazowska
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Correspondence to Dorota Głazowska.

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Głazowska, D. A solution of an open problem concerning Lagrangian mean-type mappings. centr.eur.j.math. 9, 1067–1073 (2011). https://doi.org/10.2478/s11533-011-0059-2

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  • DOI: https://doi.org/10.2478/s11533-011-0059-2

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