Banach空间中平均非扩张集值映射的稳定点

摘要

The fixed point theory of the set-valued mappings has important applications in many branches such as modern variation problems, optimization problems and economic equilibrium problems, and it has been an essential part of nonlinear functional analysis theory. In order to study the problem of the stationary points of the mean nonexpansive set-valued mappings in Banach spaces, we based on Fixed Point Theory of the set-valued mapping,by use of the asymptotic stationary points sequence,the asymptotic center and the asymptotic radius,the necessary and sufficient conditions for the mean nonexpansive set-valued mappings which have the stationary points are obtained.%集值映射的不动点理论在近代变分问题、最优化问题、经济均衡问题等研究中发挥着极其重要的作用,已成为非线性泛函分析理论的重要组成部分.为了研究Banach空间中平均非扩张集值映射的稳定点问题,我们依据集值映射的不动点理论,利用渐近稳定点序列、渐近中心、渐近半径等给出了平均非扩张集值映射具有稳定点的充分必要条件.