分形集上调和(p, s)-凸函数的Jensen和Jensen-Mercer不等式及其应用

Jensen and Jensen-Mercer Inequalities for Harmonic (p, s)-Convex Functions on Fractal Sets and Their Applications

首次提出分形集上调和(p, s)-凸函数的定义,建立了该函数的广义Jensen不等式和广义Jensen-Mercer不等式。引入局部分数阶积分,利用构建的Jensen不等式和Jensen-Mercer不等式,得到了广义调和(p, s)-凸函数的Hermite-Hadamard不等式。最后,讨论了部分结果在概率中的一些应用。

For the first time, the definition of harmonic (p, s)-convex functions on fractal sets is proposed. The generalized Jensen inequality and the generalized Jensen-Mercer inequality for the functions are established. By introducing local fractional order integrals and the constructed Jensen and Jensen-Mercer inequalities, the Hermite-Hadamard inequality for generalized harmonic (p, s)-convex functions is derived. Finally, applications of some results in probability are discussed.