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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


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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
PII: S 0002-9939(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.