Lipschitz-continuity of Spherically Convex Functions

被引：0
作者：
Yin Zhang
Qi Guo
机构：
[1] Suzhou University of Science and Technology,Department of Mathematics
来源：
Acta Mathematica Sinica, English Series | 2023年 / 39卷
关键词：
Spherically convex set; spherically convex function; Lipschitz-continuity; uniform convergence; 52A55;
D O I：
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中图分类号：
学科分类号：
摘要：
In this article, some basic and important properties of spherically convex functions, such as the Lipschitz-continuity, are investigated. It is shown that, under a weaker condition, every family of spherically convex functions is equi-Lipschitzian on each closed spherically convex subset contained in the relative interior of their common domain, and from which a powerful result is derived: the pointwise convergence of a sequence of spherically convex functions implies its uniform convergence on each closed spherically convex subset contained in the relative interior of their common domain.
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页码：363 / 374
页数：11
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