Hilbert格上的极小不动点定理及其在不连续变分不等式中的应用(英文)  

Minimal Fixed Point Theorem and its Applications to Discontinuous Variational Inequalities in Hilbert Lattices

作　　者：王月虎[1] 刘保庆[2] 

机构地区：[1]南京财经大学管理科学与工程学院,江苏南京210023 [2]南京财经大学应用数学学院,江苏南京210023

出　　处：《应用数学》2016年第1期152-160,共9页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11071109,11401296);the Jiangsu Provincial Natural Science Foundation of China(BK20141008);the Natural Science Fund for Colleges and Universities in Jiangsu Province(14KJB110007)

摘　　要：本文在Hilbert空间中利用Zorn引理的对偶定理获得下保序集值映射的极小不动点定理.利用该不动点定理证明广义变分不等式问题极小解的存在性.此外,还研究广义变分不等式问题解映射的下保序性.与其他多数研究变分不等式的方法相比,本文的方法是序方法,故不需要相关映射具有拓扑连续性.In this paper, we use the dual version of Zorn＇s lemma to obtain a minimal fixed point theorem for lower order-preserving set-valued mappings in Hilbert lattices. Ap- plying this fixed point theorem, we introduce an existence theorem of minimal solutions to generalized variational inequalities. Furthermore, we also study the lower order-preservation of solution correspondence for parametric generalized variational inequalities. In contrast to many papers on variational inequalities, our approach is order-theoretic and the results obtained in this paper do not involve any topological continuity with respect to the considered mappings.

关 键 词：极小不动点 保序性 Hilbert格 广义变分不等式 

分 类 号：O177.91[理学—数学]