Inequalities and means from a cyclic differential equation

• Autorzy: Herzog G. , Kunstmann P.
• Języki publikacji: EN

Abstrakty

EN

We prove that the solution of the cyclic initial value problem (…) is convergent to an equilibrium (…) , and study the properties of the function (…) and its relation to Shapiro’s inequality.

Słowa kluczowe

EN

Shapiro inequality; cyclic differential equation; quasimonotonicity

PL

nierówność Shapiro; cykliczne równanie różniczkowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 2
• Strony: 300--309
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Herzog G.

• Institut Für Analysis, Karlsruher Institut Für Technologie (Kit), D-76128 Karlsruhe, Germany

autor

Kunstmann P.

• Institut Für Analysis, Karlsruher Institut Für Technologie (Kit), D-76128 Karlsruhe, Germany

Bibliografia

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• [3] A. Clausing, A review of Shapiro’s cyclic inequality, General inequalities 6, Proc. 6th Int. Conf., Oberwolfach/Ger. 1990, 17–31, (1992).
• [4] P. Hartman, Ordinary Differential Equations, Philadelphia, PA: SIAM, (2002).
• [5] D. S. Mitrinovic, J. E. Pecaric, A. M. Fink, Classical and New Inequalities in Analysis, Dordrecht, Kluwer Academic Publishers, (1993).
• [6] S. H. Shapiro, Advanced problem 4603, Amer. Math. Monthly 61 (1954), 571.
• [7] P. Volkmann, Über die Invarianz konvexer Mengen und Differentialungleichungen in einem normierten Raume, Math. Ann. 203 (1973), 201–210.
• [8] W. Walter, Differential and Integral Inequalities, Berlin-Heidelberg-New York, Springer-Verlag, (1970).