Volume 3,  Issue 5, 2002

Article 82



E-Mail: r.a.satnoianu@city.ac.uk

Received 10 July, 2002; Accepted 5 August, 2002.
Communicated by: C.P. Niculescu

ABSTRACT.   We consider a class of algebraic inequalities for functions of n variables depending on parameters that generalise the case of GA-convex functions. The functions in this class are GA-convex only in a subdomain of definition yet the inequality for GA-convexity still holds on the whole domain if suitable conditions are satisfied by the parameters. The method is elementary and allows us to give further extensions to a large class of functions.

As an application we show the validity of an n-dimensional generalization of a conjectured inequality related to a problem given at the 42nd IMO held in Washington DC (USA) in 2001.

Key words:
Convex functions, GA-convexity, Symmetric functions, IMO competition.

2000 Mathematics Subject Classification:
26D15, 26D10, 39B62, 52A40.

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

Integral Means Inequalities for Fractional Derivatives of Some General Subclasses of Analytic Functions
Tadayuki Sekine, Kazuyuki Tsurumi, Shigeyoshi Owa and H.M. Srivastava

Operator-Splitting Methods for General Mixed Variational Inequalities
Muhammad Aslam Noor

Ostrowski Type Inequalities for Isotonic Linear Functionals
S.S. Dragomir

A Note on Aczel Type Inequalities
Vania Mascioni

On Short Sums of Certain Multiplicative Functions
Olivier Bordellès

A Monotonicity Property of Ratios of Symmetric Homogeneous Means
Peter A. Hästö

Coefficient Estimates for Certain Classes of Analytic Functions
Shigeyoshi Owa and Junichi Nishiwaki

A Monotonicity Property of the Gamma Function
Hendrik Vogt and Jürgen Voigt

A Holder-type Inequality for Positive Functionals on F-Algebras
Karim Boulabiar

A New Inequality Similar to Hilbert's Inequality
Bicheng Yang

Extensions of Hiong's Inequality
Ming-liang Fang and Degui Yang

New Upper and Lower Bounds for the Cebysev Functional
P. Cerone and S.S. Dragomir

A Note on the Trace Inequality for Products of Hermitian Matrix Power
Zhong Peng Yang and Xiao Xia Feng

Pointwise Error Estimate for a Noncoercive System of Quasi-Variational Inequalities Related to The Management of Energy Production
Messaoud Boulbrachene

Reverse Convolution Inequalities and Applications to Inverse Heat Source Problems
Saburou Saitoh, Vu Kim Tuan and Masahiro Yamamoto

Sufficient Conditions for Starlike Functions of Order a
V. Ravichandran, C. Selvaraj and R. Rajalaksmi

Improved GA- Convexity Inequalities
Razvan A. Satnoianu

Strong Convergence Theorems for Iterative Schemes with Errors for Asymptotically Demicontractive Mappings in Arbitrary Real Normed Linear Spaces
Yeol Je Cho, Haiyun Zhou and Shin Min Kang

Asymptotic Expansion of the Equipoise Curve of a Polynomial Inequality
Roger B. Eggleton and William P. Galvin


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.