Brouwer不动点定理的推广及其应用

AN EXTENSION OF BROUWER'S FIXED POINT THEOREM AND ITS APPLICATION

本文证明了当算子定义域的要求由紧凸集放宽到紧星形体时,Brouwer不动点定理的结论仍然成立,作为推广的Brouwer不动点定理的一个应用,得到了一类非线性方程组解的存在性的一个新结果.

In this paper,it is proved that the Brouwer fixed point theorem remains valid if we replace a compact convex set by a compact star body.As an application,a new existence theorem for a class of a system of nonlinear equations is obtained.