In this paper, the standard Jensen inequality for two points and convex functions is generalized to a version for four points satisfying Sherman’s majorization condition and for G-invariant convex functions, where G is a subgroup of the orthogonal group acting on an inner product space. A control map is used. A comparison of the obtained inequality and Jensen inequality is presented.

中文翻译：

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具有G不变凸函数的控制映射的Jensen-Sherman型不等式

在本文中，将两点和凸函数的标准Jensen不等式推广为满足Sherman主化条件的四点和G不变凸函数的一个版本，其中G是作用在内积空间上的正交群的子群。使用控制图。给出了获得的不等式和詹森不等式的比较。