On Stationary Points of Mean Nonexpansive Set-valued Mappings in Banach Spaces - CHEN Li-li; GAO Lu; ZHOU Jing (Journal of Harbin University of Science and Technology)
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.