Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
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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

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