广义强(s,m)-凸函数的simpson型积分不等式

Simpson Type Integral Inequalities for Generalized Strong(s,m)-convex Functions

凸函数是数学学科中一类重要的函数,由凸函数理论发展起来的凸分析是逼近论、控制论、系统理论、运筹学等学科的重要基础理论之一.目前凸函数的主要研究内容包括凸函数的性质、积分不等式以及凸函数的推广.本文研究了广义强(s,m)-凸函数的simpson型积分不等式问题.建立新的积分等式,利用Hölder不等式和分析理论方法得到了关于广义强(s,m)-凸函数的一些新的simpson型不等式.

The convex function is important in mathematics.Convex analysis developed by convex function theory is one of the important basic theories of approximation,cybernetics,system theory,operations research and other disciplines.At present,the main research in convex functions includes the properties of convex functions,inte⁃gral inequalities and the generalization of convex functions.The simpson type integral inequality problem of gen⁃eralized strong(s,m)-convex functions was studied and a new integral equation was established.Some new Simpson type inequalities for generalized strong(s,m)-convex functions were obtained using Hölder’s inequali⁃ty and analytical theory.