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Inequalities for the weighted mean of  -convex functions
Author(s):
Mingbao
Sun;
Xiaoping
Yang
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1639-1646.
MSC (2000):
Primary 26D15, 26A51
Posted:
January 25, 2005
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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.
References:
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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:
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
Posted:
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
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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