In this paper we first introduce the Heron and Heinz means of two convex functionals. Afterwards, some inequalities involving these functional means are investigated. The operator versions of our theoretical functional results are immediately deduced. We also obtain new refinements of some known operator inequalities via our functional approach in a fast and nice way.

中文翻译：

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涉及两个凸泛函的 Heron 和 Heinz 均值的一些不等式

在本文中，我们首先介绍了两个凸泛函的 Heron 和 Heinz 均值。然后，研究了涉及这些功能手段的一些不等式。我们的理论函数结果的算子版本立即被推导出来。我们还通过我们的函数方法以一种快速而漂亮的方式获得了一些已知算子不等式的新改进。