局部Lipschitz全连续弱内向映象的新不动点定理

New Fixed Point Theorems of Locally Lipschitz Completely Continuous and Weakly Inward Maps

利用有界凸闭集上局部Lipschitz全连续弱内向映象的不动点指数一个基本结论,得到了有界凸闭集上局部Lipschitz全连续弱内向映象的新不动点定理.特别地,得到了有界凸闭集上局部Lipschitz全连续弱内向映象的Altman定理,Roth定理和Petryshyn定理及其各种推广形式.

In this paper, based on a basic result on locally Lipschitz completely continuous and weakly inward maps, some new fixed point theorems of locally Lipschitz completely continuous and weakly inward maps defined on a closed bounded convex set are obtained. As a result, the famous Altmaffs theorem, Roth＇s theorem and Petryshyn＇s theorem for such class of mappings are obtained and generalized.