AR凸函数的Hermite-Hadamard型不等式

建立AR凸函数的积分不等式,特别是Hermite-Hadamard型不等式.利用通常凸函数与AR凸函数的关系,证明了AR凸函数的单侧导数的存在性和单调性,并通过不等式建立了AR凸函数与其单侧导数的关系.从AR凸函数的定义出发,得到了AR凸函数的Hermite-Hadamard型不等式.利用AR凸函数与其单侧导数的关系,使用数学分析的方法,研究了由AR凸函数的Hermite-Hadamard型不等式生成的差值.利用AR凸函数与其单侧导数的关系,构造了与AR凸函数有关的单调函数,从而给出AR凸函数的定积分的上界和下界.另外,利用AR凸函数与其单侧导数的关系,还建立了AR凸函数的其他的积分不等式.

Hermite-Hadamard Type Inequalities for AR-Convex Functions

The integral inequalities of AR-convex functions, especially the Hermite-Hadamard inequalities, are established. With the aid of the relationship between convex functions and AR-convex functions, the existence and monotonicity of unilateral derivatives of AR-convex functions are proved, and the relationship between AR-convex functions and their unilateral derivatives is established through inequalities. Starting from the definition of AR-convex functions, the Hermite-Hadamard type inequalities for AR-convex functions are obtained. By using the relationship between AR-convex functions and their unilateral derivatives or using mathematical analysis, the difference generated by the Hermite-Hadamard type inequality of AR-convex functions is studied. By using the relationship between AR-convex functions and their unilateral derivatives, the monotone function related to AR-convex functions is constructed, and the upper and lower bounds of the definite integral of AR-convex function are given. In addition, by using the relationship between AR-convex functions and their unilateral derivatives, other integral inequalities of AR-convex functions are established.