Order-preservation of solution correspondence for parametric generalized variational inequalities on Banach lattices

Fixexd point theory and applications

Congjun Zhang¹  Yuehu Wang² 

[1] School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, P.R. China;School of Management Science and Engineering, Nanjing University of Finance and Economics, Nanjing, P.R. China

关键词: order-theoretic fixed point;    order-preservation;    parametric generalized variational inequalities;    equilibrium problems;    Banach lattices;   

DOI  :  10.1186/s13663-015-0360-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, several order-theoretic fixed point theorems are proved on Banach lattices. As applications of these fixed point theorems, we study the order-preservation of solution correspondence for parametric generalized variational inequalities. Furthermore, the existence of solutions to equilibrium problems is also examined. Our approach is order-theoretic and all results obtained in this paper do not require the considered mappings to be continuous or semi-continuous with respect to any topology equipped on the underlying space.

【 授权许可】

CC BY