An invariance of the geometric mean with respect to Lagrangian conditionally homogeneous mean-type mappings

• Autorzy: Głazowska D.
• Języki publikacji: EN

Abstrakty

EN

We determine all the Lagrangian conditionally homogeneous mean-type mappings for which the geometric mean is invariant.

Słowa kluczowe

EN

Lagrangian mean; conditionally homogeneous mean; functional equations; iterate

PL

średnia Lagrangiana; średnia warunkowo homogeniczna; równania funkcyjne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2007
• Tom: Vol. 40, nr 2
• Strony: 289--302
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Głazowska D.

• Department of Mathematics Computer Science and Econometrics University of Zielona Góra 65-512 Zielona Góra, Poland,

Bibliografia

• [1] J. Błasińska-Lesk, D. Głazowska, J. Matkowski, An invariance of the geometric mean with respect to Stolarsky mean-type mappings, Result. Math. 43 (2003), 42-55.
• [2] J. M. Borwein, P. B. Borwein, Pi and the AGM - A study in Analytic Number Theory and Computational Complexity, A Wiley - Interscience Publication, John Wiley &; Sons, New York - Chichester - Brisbane - Toronto - Singapore (1987).
• [3] P. S. Bullen, D. S. Mitrinović, P. M. Vasić, Means and Their Inequalities, Mathematics and its Applications, D. Reidel Publishing Company, Dordrecht-Boston-Lancaster-Tokyo (1988).
• [4] J. Jarczyk, J. Matkowski, Invariance in the class of weighted quasi-arithmetic means, Ann. Polon. Math. 88 (2006), 39-51.
• [5] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, PWN (1985).
• [6] J. Matkowski, Iterations of mean-type mappings and invariant means, Ann. Math. Sil. 13 (1999), 211-226.
• [7] J. Matkowski, Mean value property and associated functional equations, Aequationes Math. 58 (1999), 46-59.
• [8] J. Matkowski, Lagrangian mean-type mappings for which the arithmetic mean is invariant, J. Math. Anal. Appl. 309 (2005), 15-24.