涉及可微(α,m)凸函数的单调函数和Hermite-Hadamard型不等式

Monotonic Functions and Hermite-Hadamard Type Inequalities Involving Differentiable(α,m)-Convex Functions

利用第一种意义上的(α,m)凸函数与其导函数的关系,证明几个与第一种意义上的(α,m)凸函数有关的单调函数,建立几个Hermite-Hadamard型不等式.通过建立涉及一阶导数的恒等式,利用(α,m)凸函数的定义,针对其导数的绝对值为(α,m)凸函数的可微函数,建立Hermite-Hadamard型不等式.

Using the relationship between（ α,m）-convex functions in the first sense and its derivative functions,we prove several monotone functions related to（ α,m）-convex functions in the first sense and establish several Hermite-Hadamard type inequalities. By establishing the identity involving the first derivative and using the definition of（ α,m）-convex functions,Hermite-Hadamard type inequalities are obtained for differentiable functions whose absolute value of the derivative are（ α,m）-convex functions.