分数次积分下关于s-凸函数的新Hermite-Hadamard型不等式

摘要

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.