一个有限渐近拟非扩张映射族的收敛定理

Convergence Theorem for a Finite Family of Asymptotically Nonexpansive Mappings

在一致凸的Banach空间中,研究有限渐近拟非扩张映射族的Mann迭代和多步Ishikawa型迭代序列的收敛性,并对一些已有的Mann迭代和多步Ishikawa型迭代序列进行进一步地推广和统一.在实数空间中,构造一个非负实序列,使得这个非负实序列是收敛的,从而利用这个非负实序列的收敛性证明该迭代序列在一定条件下强收敛到有限渐近拟非扩张映射族的公共不动点.

Finite asymptotically nonexpansive Mann iterative and multi-step Ishikawa type iterative sequence of convergentare are investigated in the uniformly convex Banach space,and some Mann iterations and multi-step Ishikawa type iterative sequences are popularized.In the real space,a convergent non-negative real sequence is constructed,and it＇s convergent.Under certain conditions,the iterative sequence is proved that it converges strongly to the common fixed point of a finite family of asymptotically nonexpansive mappings.