In the article, we establish several inequalities for the generalized weighted mean values of g-convex functions. As applications, we provide several new Hermite-Hadamard type inequalities for the g-convex functions. Our results are the generalizations of some previously known results.

中文翻译：

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g-凸函数的广义加权平均值的不等式与应用

在文章中，我们为 g-凸函数的广义加权平均值建立了几个不等式。作为应用程序，我们为 g-凸函数提供了几个新的 Hermite-Hadamard 型不等式。我们的结果是一些先前已知结果的概括。