分数次积分下关于s-凸函数的新Hermite-Hadamard型不等式

New Hermite-Hadamard-type inequalities for s-convex functions via fractional integrals

建立了一个关于Riemann-Liouville分数次积分的恒等式,利用此恒等式,得到了一些函数为可微且s-凸映射的关于分数次积分的新Hermite-Hadamard型积分不等式,并且对于可微的s-凹函数也得到一些新的结果.文中的新结果推广了部分已有研究的结论.最后给出了一个应用实例.

In this paper,we establish a new identity for Riemann-Liouville fractional integrals.Using the established identity,some new Hermite-Hadamard type inequalities for differentiable s-convex mappings that are connected with the Riemann-Liouville fractional integrals are obtained.Also,some results are deduced for differentiable s-concave functions.Our results extend some proved results in the existing researches.Finally,we give an example to illustrate the applications of the results.