Banach空间中一类算子的强收敛定理

Strong Convergence Theorem of One Kind of Operator in Banach Spaces

研究了自反的Banach空间中非空凸非扩展保核收缩序列的M收敛性问题 ,主要证明了 :设E是自反的Banach空间 ,B是E的闭凸子集 ,{Cn}是B的非空凸的非扩展保核收缩序列 ,若C0 =M -limnCn存在且非空 ,则C0 是B的非扩展保核收缩凸核 .

Study the Mosco convergence of a sequence of nonempty convex nonexpansive retracts in a reflexive Banach space.It's Proved that the mainly result as follows:Let B be a closed convex subset of a reflexive Banach space E,and ｛C n｝ be a sequence of nonempty convex nonexpansive retracts of B.If C 0=M-lim n?C n exists and is nonempty,then C 0 is a convex nonexpansive retract of B.