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Vietnam Journal of Mathematics 40:4(2012) 505-514

 

Some Inequalities for Differentiable Functions and Applications

Zheng Liu

Institute of Applied Mathematics, School of Science, University of Science and

Technology Liaoning, Anshan 114051, Liaoning, China

Received July 28, 2011

Revised February 8, 2012

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.

2000 Mathematics Subject Classification. 26D15.

Keywords. Hölder inequality, averaged midpoint-trapezoid inequality, convex function, concave function, special means, numerical integration

 

 

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