Banach空间中非Lipschitz映象的连续半群的不动点定理  

Fixed Point Theorem for Continuous Semigroups of Non-Lipschitzian Mappings in Banach Spaces

作　　者：曾六川[1] 

机构地区：[1]上海师范大学数学系,上海200234

出　　处：《数学学报（中文版）》2002年第4期737-744,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助(19801023);国家教育部高等学校优秀青年教师教学和科研奖励基金资助项目

摘　　要：设E是一实的p一致凸Banach空间.利用渐近中心,E中范数不等式和逐次逼近的思想,本文证明了E中非Lipschitz映象的连续半群的不动点存在的定理.该定理本质上把Lipschitz半群的不动点存在性的研究推广到了非Lipschitz映象的连续半群的情况.另一方面,应用该定理,还得到了非Lipschitz映象的渐近非扩张型半群的渐近行为方面的一些结果.The purpose of this paper is to prove a fixed point existence theorem for continuous semigroups of non-Lipschitzian mappings in a real p-uniformly convex Ba-nach space E by exploiting the idea of asymptotic centers, norm inequalities in E, and successive approximations. This theorem essentially extends and generalizes the investigation of the fixed point existence for Lipschitzian semigroups to the case of continuous semigroups of non-Lipschitzian mappings. On the other hand, using this theorem, the author obtains some results on the asymptotic behavior of asymptotically nonexpansive type semigroups of non-Lipschitzian mappings.

关 键 词：不动点 连续半群 非Lipschitz映象 p一致凸Banach空间 

分 类 号：O177.91[理学—数学]