A counterpart of the Ohlin theorem for convex set-valued maps is proved. An application of this result to obtain some inclusions related to convex set-valued maps in an alternative unified way is presented. In particular counterparts of the Jensen integral and discrete inequalities, the converse Jensen inequality and the Hermite–Hadamard inequalities are obtained.

中文翻译：

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凸集值映射的 Ohlin 型定理

证明了凸集值映射的 Ohlin 定理的对应物。介绍了该结果在以替代的统一方式获得与凸集值映射相关的一些包含的应用。在 Jensen 积分不等式和离散不等式的特定对应项中，可以得到逆 Jensen 不等式和 Hermite-Hadamard 不等式。