Banach空间上的不连续映射的不动点定理

Fixed Point Theorems for Discontinuous Mapping in Banach Spaces

本文把著名的Ｓｃｈａｕｄｅｒ定理推广到不连续映射的情形，主要的结果表明对任一Ｂａｎａｃｈ空间中的任一给定的紧凸子集上的任一自映射，可以在紧凸集上找一点ｘ，使‖ｘ－ｆ（ｘ）‖不超过函数的固定的不连续测量。

In this paper, we prove a generalization of Schauder′s fixed point theorem for discontinuous maps. The main result shows that for discontinuous functions on a compact convex domain X of a Banach spaces E, one can always find a point x∈X such that |x-f(x)| is less than a certain measure of discontinuity. This result is a generalization of Schauder′s theorem and .