Logarithmic convexity of extended mean values

Author:
Feng Qi

Journal:
Proc. Amer. Math. Soc. **130** (2002), 1787-1796

MSC (2000):
Primary 26A51; Secondary 26B25, 26D07

Published electronically:
December 20, 2001

MathSciNet review:
1887027

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this article, the logarithmic convexity of the extended mean values are proved and an inequality of mean values is presented. As by-products, two analytic inequalities are derived. Two open problems are proposed.

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Additional Information

**Feng Qi**

Affiliation:
Department of Mathematics, Jiaozuo Institute of Technology, Jiaozuo City, Henan 454000, People’s Republic of China

Email:
qifeng@jzit.edu.cn

DOI:
http://dx.doi.org/10.1090/S0002-9939-01-06275-X

Keywords:
Logarithmic convexity,
extended mean values,
inequality,
exponential function,
absolutely monotonic function

Received by editor(s):
May 31, 2000

Received by editor(s) in revised form:
December 26, 2000

Published electronically:
December 20, 2001

Additional Notes:
The author was supported in part by NSF of Henan Province (no. 004051800), SF for Pure Research of the Education Department of Henan Province (no. 1999110004), SF for the Prominent Youth of Henan Province, Doctor Fund of Jiaozuo Institute of Technology, SF of Henan Innovation Talents at Universities, and NNSF (no. 10001016) of China

Communicated by:
Carmen C. Chicone

Article copyright:
© Copyright 2001
American Mathematical Society