In certain case it might be necessary to further decompose a spiral into convex subsets . 在某些情況下,把一個螺旋形進一步分解成凸子集是必要的。
A relatively optimal compact convex subset of continuous games 連續對策的相對最優緊凸策略子集
The maximal value point s problem of a convex function on a closed convex subset in locally convex space is considered by using the level set of function , - subdifferential and - normal cone . it gives several equivalent characters on the optimal solutions of the problem 利用函數的水平集, -次微分和-法向錐等工具研究局部凸空間的凸函數在閉凸子集上的最大值點問題,給出了最優解的幾個等價刻劃
Throughout the following of this section , e denotes a real banach space and p is a cone in e . in chapter , a new three - solution theorem is obtained . moreover , the famous amann ' s and leggett - williams " three - solution theorems in nonlinear functional analysis can be seen as its special cases , namely they are united . so they are improved . the main results can be stated as the following : let d be a nonempty bounded close convex subset in e , and nonnegative continuous functional on d . and is concave while is convex . suppose 0 < d and denote 首先我們約定,在下文中, e是實banach空間, p是e中的錐。在第一章中,我們利用錐理論與不動點指數理論統一了著名的amann三解定理與leggett - williams三解定理。主要結論是:設d是e中的非空有界閉凸集, ,是d上的非負連續泛函,且是凹泛函,是凸泛函。