Volume 3,  Issue 3, 2002

Article 40

A MONOTONICITY PROPERTY OF POWER MEANS

A.MCD. MERCER

DEPARTMENT OF MATHEMATICS AND STATISTICS,
UNIVERSITY OF GUELPH, 
GUELPH, ONTARIO, N1G 1J4 
CANADA.
E-Mail: amercer@reach.net

Received 21 February, 2002; Accepted 24 March, 2002.
Communicated by: P. Bullen


ABSTRACT.    If $ A$ and $ G$ are the arithmetic and geometric means of the numbers $ %%
x_{j}\in (a,b)$, a family of inequalities is derived of which $ a+b-A>ab/G$ is a special case. These inequalities demonstrate a new monotonicity property for power means.
Key words:
Arithmetic mean, Geometric mean, Monotonicity, Power means.

2000 Mathematics Subject Classification:
26D15.


Download this article (PDF):

Suitable for a printer:    

Suitable for a monitor:        

To view these files we recommend you save them to your file system and then view by using the Adobe Acrobat Reader. 

That is, click on the icon using the 2nd mouse button and select "Save Target As..." (Microsoft Internet Explorer) or "Save Link As..." (Netscape Navigator).

See our PDF pages for more information.

 

Other papers in this issue

An Inequality which Arises in the Absence of the Mountain Pass Geometry
Radu Precup 

On the Hyers-Ulam Stability of Quadratic Functional Equations 
Ick-Soon Chang and Hark-Mahn Kim

Projection Iterative Schemes for General Variational Inequalities
M. Aslam Noor, Y.Wang and N.Xiu

An Inequality Improving the Second Hermite-Hadamard Inequality for Convex Functions Defined on Linear Spaces and Applications for Semi-Inner Products
S.S. Dragomir 

Multivalued Quasi Variational Inequalities in Banach Spaces
M. Aslam Noor, A. Moudafi and B. Xu

On an Inequality Related to the Legendre Totient Function
Pentti Haukkanen

Explicit Upper Bounds for the Average Order of dn and Applications to Class Number
O. Bordelles

Iterated Turan and Laguerre Inequalities
Thomas Craven and George Csordas

A Monotonicity Property of Power Means
A.McD. Mercer

Moment Inequalities of a Random Variable Defined over a Finite Interval
Pranesh Kumar 

Some Generalized Convolution Properties Associated with Certain Subclasses of Analytic Functions
S. Owa and H.M. Srivastava

Inequalities on Linear Functions and Circular Powers
Pantelimon Stanica

Bounding the Maximum Value of the Real-Valued Sequence
Eugene V. Dulov and Natalia A. Andrianova

An Inequality of the 1-D Klein-Gordon Equation with a Time-varying Parameter
Iwan Pranoto

Weak Periodic Solutions of Some Quasilinear Parabolic Equations with Data Measures
N. Alaa and M. Iguernane 

Bounds on Certain Integral Inequalities
B.G. Pachpatte

 

Other issues

 

2000 School of Communications and Informatics, Victoria University of Technology. All rights reserved.
JIPAM is published by the School of Communications and Informatics which is part of the Faculty of Engineering and Science, located in Melbourne, Australia. All correspondence should be directed to the editorial office.

Copyright/Disclaimer