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2011 | 9 | 5 | 1067-1073
Tytuł artykułu

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

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Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
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Czasopismo
Rocznik
Tom
9
Numer
5
Strony
1067-1073
Opis fizyczny
Daty
wydano
2011-10-01
online
2011-07-26
Twórcy
Bibliografia
  • [1] Borwein J.M., Borwein P.B., Pi and the AGM, Canad. Math. Soc. Ser. Monogr. Adv. Texts, John Wiley & Sons, New York-Chichester-Brisbane-Toronto-Singapore, 1987
  • [2] Bullen P.S., MitrinoviĆ D.S., VasiĆ P.M., Means and Their Inequalities, Math. Appl. (East European Ser.), 31, D. Reidel, Dordrecht-Boston-Lancaster-Tokyo, 1988
  • [3] Daróczy Z., Páles Zs., Gauss-composition of means and the solution of the Matkowski-Sutô problem, Publ. Math. Debrecen, 2002, 61(1–2), 157–218
  • [4] Głazowska D., Some Cauchy mean-type mappings for which the geometric mean is invariant, J. Math. Anal. Appl., 2011, 375(2), 418–430 http://dx.doi.org/10.1016/j.jmaa.2010.09.036
  • [5] Głazowska D., Matkowski J., An invariance of geometric mean with respect to Lagrangian means, J. Math. Anal. Appl., 2007, 331(2), 1187–1199 http://dx.doi.org/10.1016/j.jmaa.2006.09.005
  • [6] Matkowski J., Invariant and complementary quasi-arithmetic means, Aequationes Math., 1999, 57(1), 87–107 http://dx.doi.org/10.1007/s000100050072
  • [7] Matkowski J., Iterations of mean-type mappings and invariant means, Ann. Math. Sil., 1999, 13, 211–226
  • [8] Matkowski J., On invariant generalized Beckenbach-Gini means, In: Functional Equations - Results and Advances, Adv. Math. (Dordr.), 3, Kluwer, Dordrecht, 2002, 219–230
  • [9] Matkowski J., Lagrangian mean-type mappings for which the arithmetic mean is invariant, J. Math. Anal. Appl., 2005, 309(1), 15–24 http://dx.doi.org/10.1016/j.jmaa.2004.10.033
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0059-2
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