Inequalities for the weighted mean of -convex functions

Authors:
Mingbao Sun and Xiaoping Yang

Journal:
Proc. Amer. Math. Soc. **133** (2005), 1639-1646

MSC (2000):
Primary 26D15, 26A51

Published electronically:
January 25, 2005

MathSciNet review:
2120261

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, the inequalities for the weighted mean of -convex functions are established. As applications, inequalities between the two-parameter mean of an -convex function and extended mean values are given.

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Additional Information

**Mingbao Sun**

Affiliation:
Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, People’s Republic of China – and – Department of Applied Mathematics, Hunan Institute of Science and Technology, Yueyang 414000, Hunan, People’s Republic of China

Email:
sun_mingbao@163.com

**Xiaoping Yang**

Affiliation:
Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, People’s Republic of China

DOI:
http://dx.doi.org/10.1090/S0002-9939-05-07835-4

Keywords:
Inequality,
$r$-convex function,
weighted mean,
two-parameter mean,
extended mean values,
Tchebycheff integral inequality,
standard mollifier

Received by editor(s):
March 27, 2003

Published electronically:
January 25, 2005

Additional Notes:
This research was supported in part by SF for Pure Research of Natural Sciences of the Education Department of Hunan Province (no.2000C315), and NNSF (no.10271071) of China.

Communicated by:
Carmen C. Chicone

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.