Journal of Shanghai University(Natural Science Edition) ›› 2017, Vol. 23 ›› Issue (4): 583-589.doi: 10.12066/j.issn.1007-2861.1716

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Hadamard-type inequalities for a class of (α ,m)-convex functions

LI Yujiao1, DU Tingsong1,2   

  1. 1. College of Science, China Three Gorges University, Yichang 443002, Hubei, China;
    2. Hubei Province Key Laboratory of System Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430081, China
  • Received:2015-06-01 Online:2017-08-30 Published:2017-08-30

Abstract:

This paper proposes an integral identity. Based on the identity, some results of Hadamard inequalities are established for functions with the q-th power of the second derivative’s absolute value (α,m)-convex. Some specific applied examples are presented.

Key words: Hadamard-type inequality,  (α, m)-convex function, convex function