几个h-预不变凸函数的分数阶积分不等式及在数值积分中的应用

Some fractional integrals inequalities for h-preinvex functions and applications to numerical integration

构造了一个带参数的Riemann-Liouville分数阶积分恒等式,得到几个关于h-预不变凸函数的带参数的分数阶积分不等式。当参数取特殊值时,分别得到了“中点型”“梯形型”和“Simpson型”积分不等式。利用构建的不等式得到了几个经典数值积分的误差估计式。

An identity with parameters is constructed via Riemann-Liouville fractional integrals.With that,we derive some fractional integrals inequalities with parameters for h-preinvex functions.The"midpoint type","trapezoidal type"and"Simpson type"integral inequalities are obtained respectively when the parameters are given special values.Finally,the error estimates of numerical integration are proposed to illustrate the applications of the results.