广义渐近拟非扩张映射族公共不动点的逼近

Approximation of Common Fixed Points for Finite Families of Generalized Asymptotically Quasi-Nonexpansive Mappings

设C是Banach空间E的非空闭凸子集,{Ti}ik=1为C上的一族广义渐近拟非扩张自映射,f:C→C为压缩映射,Wn为修正的W-映射.引入迭代算法:xn+1=λnf(xn)+(1-λn)Wn,并证明了由此产生的迭代序列{xn}强收敛到T1,T2,…,Tk的一个公共不动点.

Let C be a nonempty closed convex subset of a Banach space E, {Ti}i-1^k is a finite family of generalized asymptotically quasi-nonexpansive mappings of C into itself, f is a fixed contractive mapping, and Wn, is a modified W -mapping. We introduce an iterative method defined by xn＋1=λnf（xn）＋（1-λn）Wn, and prove that the iterative sequence {xn } converges strongly to a common fixed point of T1,T2,…,Tk.