Abstract: In strictly convex Banach space，there is set F(T)of coupled fixed points of T for nonexpansive mapping，and it is a closed convex set．When the F(T)becomes the closed linear subspace of the Hilbert space，the relationship of the elements of best approximation between the limit element and initial element of Ishikawa iteration is put forward．

Key words: nonexpansive mapping, coupled fixed point, strictly convex, element of the best approximation

摘要： 在严格凸Banach空间中研究了非扩张映象 的耦合不动点集F(T)的闭凸性，获得了当F(T)是Hilbert空间 中的闭线性子空间时，Ishikawa迭代的极限元与其初始元的最佳逼近元之间的关系．

关键词: 非扩张映象, 耦合不动点, 严格凸, 最佳逼近元