In this article, we investigate the concepts of monotonicity, Schur-geometric convexity, Schur-harmonic convexity, and Schur-power convexity for the lower and upper limits of the integral mean, focusing on convex functions on coordinate axes. Furthermore, we introduce novel and fascinating inequalities for binary means as a practical application.

中文翻译：

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坐标上凸函数的积分均值的 Schur-power 凸性

在本文中，我们研究了积分均值下限和上限的单调性、Schur 几何凸性、Schur 调和凸性和 Schur 幂凸性概念，重点关注坐标轴上的凸函数。此外，我们还介绍了二元均值的新颖且有趣的不等式作为实际应用。