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 functi...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.展开更多
基金Supported by the National NSF of China(Grant Nos.12071334,11671293)。
文摘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.
