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

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.