Power means generated by some mean-value theorems

Author:
Janusz Matkowski

Journal:
Proc. Amer. Math. Soc. **139** (2011), 3601-3610

MSC (2010):
Primary 26A24, 26E60; Secondary 39B22

DOI:
https://doi.org/10.1090/S0002-9939-2011-10981-X

Published electronically:
March 9, 2011

MathSciNet review:
2813390

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: According to a new mean-value theorem, under the conditions of a function ensuring the existence and uniqueness of Lagrange's mean, there exists a unique mean such that

**1.**F. Hartogs,*Zur Theorie der analytischen Funktionen mehrerer unabhängiger Veränderlichen*, Math. Ann.**62**(1906), 1-88. MR**1511365****2.**M. Kuczma,*An Introduction to the Theory of Functional Equations and Inequalities. Cauchy's Equation and Jensen's Inequality*, Uniwersytet Śläski - PWN, Warszawa - Kraków - Katowice, 1985 (Second edition, edited with a preface of Attila Gilányi, Birkhäuser Verlag, Basel, 2009). MR**788497 (86i:39008)****3.**J. Matkowski,*Generalized convex functions and a solution of a problem of Zs. Páles*, Publ. Math. Debrecen,**73**/3-4 (2008), 421-460. MR**2466385 (2009i:26048)****4.**J. Matkowski,*A mean-value theorem and its applications*, J. Math. Anal. Appl.**373**(2011), 227-234. MR**2684472**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2010):
26A24,
26E60,
39B22

Retrieve articles in all journals with MSC (2010): 26A24, 26E60, 39B22

Additional Information

**Janusz Matkowski**

Affiliation:
Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Podgórna 50, PL-65246 Zielona Góra, Poland – and – Institute of Mathematics, Silesian University, Bankowa 14, PL-42007 Katowice, Poland

Email:
J.Matkowski@wmie.uz.zgora.pl

DOI:
https://doi.org/10.1090/S0002-9939-2011-10981-X

Keywords:
Mean-value theorem,
mean,
quasi-arithmetic mean,
arithmetic mean,
geometric mean,
harmonic mean,
Jensen functional equation,
differential equation.

Received by editor(s):
August 26, 2010

Published electronically:
March 9, 2011

Communicated by:
Edward C. Waymire

Article copyright:
© Copyright 2011
American Mathematical Society