Quasi-arithmetic means

Authors

  • Jan Górowski Uniwersytet Pedagogiczny im. KEN w Krakowie
  • Adam Łomnicki Uniwersytet Pedagogiczny im. KEN w Krakowie

Keywords:

Quasi-arithmetic means, inequalities involving means, extended mean values, means in geometry

Abstract

We present a list of geometric problems with solutions that lead to knownor less known means. We also prove, by elementary means, some property for so-calledquasi-arithmetic means. We use the proved result to justify some inequalities betweenthe means.

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References

Aczél, J.: 1948, On mean values, Bull. Amer. Math. Soc. 54(4), 392-400.

Aczel, J., Dhombres, J.: 1989, Functional equation in several variables, Vol. 31, Cambridge Univ. Press, Cambridge-New York-Rochelle-Melbourne-Sydney.

Galwani, L.: 1927, Dei limiti a cui tendono alcune media, Boll. Un. Math. Ital. 6, 173-179.

Głazowska, D., Jarczyk, W., Matkowski, J.: 2002, Arithmetic mean as a linear combination of two quasi-arithmetic means, Publ. Math. Debrecen 61, 455-467.

Górowski, J., Łomnicki, A.: 2010, O srednich, Ann. Univ. Paed. Cracov. Studia ad Didacticam Math. Pertinentia 3, 55-66.

Kitagawa, T.: 1934, On some class of weighted means, Proc. Phys.-Math. Soc. Japan 16(3rd series), 117-126.

Kołgomorov, A.: 1930, Sur la notion de la moyenne, Alti Accad. Naz. Lincei 12(6), 388-391.

Leach, E., Sholander, M.: 1978, Extended mean values, Amer. Math. Monthly 85, 84-90.

Leach, E., Sholander, M.: 1983, Extended mean values ii, J. Math. Appl. 92, 207-223.

Witkowski, A.: 2009, Comparison theorem for two-parameter means, Math. Inequal. Appl. 12, 11-20.

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Published

2017-07-04

How to Cite

Górowski, J., & Łomnicki, A. (2017). Quasi-arithmetic means. Annales Universitatis Paedagogicae Cracoviensis | Studia Ad Didacticam Mathematicae Pertinentia, 7, 35–43. Retrieved from https://didacticammath.uken.krakow.pl/article/view/3628

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