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Filomat 2015 Volume 29, Issue 7, Pages: 1515-1524
https://doi.org/10.2298/FIL1507515Z
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Generalization of Hermite-Hadamard inequalities involving Hadamard fractional integrals

Zhang Zhi (Guizhou University, Department of Mathematics, Guiyang, Guizhou, P.R. China)
Wei Wei (Guizhou University, Department of Mathematics, Guiyang, Guizhou, P.R. China)
Wang Jin Rong (Guizhou University, Department of Mathematics, Guiyang, Guizhou, P.R. China + Guizhou Normal College, School of Mathematics and Computer Science, Guiyang, Guizhou, P.R. China)

In this paper, we firstly give a general integral identity for once differentiable mapping involving Hadamard fractional integrals. Secondly, we use this integral identity to derive some new generalization of fractional Hermite-Hadamard inequalities through GA-convex functions via power means and integrals GG-convex functions via power means. Some applications to special means of real numbers are given.

Keywords: generalization of Hermite-Hadamard inequalities, Hadamard fractional integrals, GA-convex function, GG-convex function