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Vietnam Journal of Mathematics 40:4(2012)
505-514
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Some Inequalities for Differentiable Functions and
Applications
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Zheng Liu
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Institute
of Applied Mathematics, School of Science, University of Science and
Technology
Liaoning, Anshan 114051, Liaoning, China
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Received July 28, 2011
Revised February 8,
2012
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Abstract. Two general inequalities for functions
whose modulus of derivatives at certain powers are convex or concave are
established. Special cases with applications to special means and numerical
integration are discussed.
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2000 Mathematics
Subject Classification. 26D15.
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Keywords.
Hölder inequality, averaged midpoint-trapezoid inequality, convex function,
concave function, special means, numerical integration
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Established
by Vietnam Academy of Science and Technology &
Vietnam Mathematical Society
Published by
Springer since January 2013
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