不动点指数法研究拟变分不等式解的存在性

The Existence of Solutions for Quasi-variational Inequalities by Using the Fixed Point Index Approach

本文在自反局部一致凸光滑的Banach空间中定义了一类广义投影算子,研究广义投影算子的性质,证明了拟变分不等式问题可转化为一类不动点问题,给出了拟变分不等式不动点指数的定义,并应用不动点指数得到某些强制条件下拟变分不等式解的存在性结果。

A class of generalized projection operator is defined in this paper,and some properties of the generalized projection operator are obtained in reflexive,locally uniformly convex,smooth Banach spaces.The equivalence between the quasi-variational inequality problem and the fixed point problem is established.A concept of fixed point index of quasi-variational inequality is introduced and the fixed point index approach is applied to obtain the existence results for solutions of quasi-variational inequality problem under some conditions.