涉及无限族非扩张映象$\{T_n\}_{n=1}^\infty$的迭代算法$x_{n 1}=\alpha_{n 1}f(x_n) (1-\alpha_{n 1})T_{n 1}x_n$

Under the framework of uniformly smooth Banach spaces, Chang proved in 2006 that the sequence {xn} generated by the iteration xn＋1 =αn＋1f（xn） ＋ （1 - αn＋1）Tn＋1xn converges strongly to a common fixed point of a finite family of nonexpansive maps {Tn}, where f ： C → C is a contraction. However, in this paper, the author considers the iteration in more general case that {Tn} is an infinite family of nonexpansive maps, and proves that Chang＇s result holds still in the setting of reflexive Banach spaces with the weakly sequentially continuous duality mapping.

Iteration $x_{n 1}=\alpha_{n 1}f(x_n) (1-\alpha_{n 1})T_{n 1}x_n$ for an Infinite Family of Nonexpansive Maps $\{T_n\}_{n=1}^\infty$

Under the framework of uniformly smooth Banach spaces, Chang$^{1]}$ proved in 2006 that the sequence $\{x_n\}$ generated by the iteration $x_{n+1}= \alpha_{n+1}f(x_n)+(1-\alpha_{n+1})T_{n+1}x_n$ converges strongly to a common fixed point of a finite family of nonexpansive maps $\{T_n\}$, where $f: C\to C$ is a contraction. However, in this paper, the author considers the iteration in more general case that $\{T_n\}$ is an infinite family of nonexpansive maps, and proves that Chang's result holds still in the setting of reflexive Banach spaces with the weakly sequentially continuous duality mapping.