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On An Inequality related to Hadamard *.(Report)
- Article from:
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Tamsui Oxford Journal of Mathematical Sciences
- Article date:
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May 1, 2008
- Author:
- Yang, Gou-Sheng; Chou, Yi-Ming; Ho, Ming-In
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Copyright informationCOPYRIGHT 2008 Aletheia University. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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In the present note we establish a new inequality which in special case, reduces to a part of Hadamard's inequality.
Keywords and Phrases: Hadamard's inequality, R-convex function, Integral power mean, Logarithmic mean, Stolarsky mean.
1. Introduction
The inequalities
f ([a+b/2])[less than or equal to][1/b-a][[integral].sub.a.sup.b]f(t)dt[less than or equal to][f(a) + f(b)/2]
which hold for all convex functions f:[a,b][right arrow] R are known in the literature as Hadamard's inequalities.
If f is a positive function on [a,b] such that for all x,y [member of][a,b] and [lambda] [member of] [0,1]
f([lambda]x + (1 - [lambda])y)[lesser than or equal ...
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