Some inequalities of Hermite--Hadamard type for functions whose second derivatives are boldsymbol (\(\alpha,m\))-convex

Volume 9, Issue 1, pp 139--148 http://dx.doi.org/10.22436/jnsa.009.01.13

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Authors

Ye Shuang - College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China. Feng Qi - Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City, 300160, China. Yan Wang - College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China.

Abstract

In the paper, the authors establish a new integral identity and by this identity with the Hölder integral inequality, discover some new Hermite-Hadamard type integral inequalities for functions whose second derivatives are (\(\alpha,m\))-convex.

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Keywords

• second derivative
• Hermite-Hadamard type inequality
• (\(\alpha،m\))-convex function
• Hölder integral inequality.

MSC

•  26D15
•  26A51
•  41A55.

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