Generalizations of Lagrange and Cauchy Mean-Value theorems

• Autorzy: Matkowski J.
• Języki publikacji: EN

Abstrakty

EN

Some generalizations of the Lagrange Mean-Value Theorem and Cauchy Mean-Value Theorem are proved and the extensions of the corresponding classes of means are presented.

Słowa kluczowe

EN

mean; mean value theorem; Lagrange theorem; Cauchy theorem; generalization; Lagrange mean; Cauchy mean; logrithmic mean; Stolarsky mean

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2010
• Tom: Vol. 43, nr 4
• Strony: 765--774
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Matkowski J.

• Faculty of Mathematics Computer Science and Econometry University of Zielona Góra Podgórna 50 65-246 Zielona Góra, Poland and Institute of Mathematics Silesian University Bankowa 14 42-007 Katowice, Poland,

Bibliografia

• [1] J. M. Borwein, P. B. Borwein, Pi and the AGM, a Study in Analytic Number Theory and Computational Complexity, John Wiley & Sons Inc., New York, 1987.
• [2] P. S. Bullen, Handbook of Means and their Inequalities, Mathematics and Its Applications, Vol. 560, Kluwer Academic Publishers, Dordrecht-Boston-London, 2003.
• [3] W. Rudin, Principles of Mathematical Analysis, Third Edition, McGraw-Hill, Inc., New York, 1976.
• [4] K. B. Stolarsky, Generalizations of the logarithmic mean, Math. Mag. 48 (1975), 87–92.
• [5] K. B. Stolarsky, The power and generalized logarithmic mean, Amer. Math. Monthly 87 (1980), 545–548.