迭代逼近渐近非扩张映像不动点的一种变形格式

Strong Convergence of an Iteration Process for Asymptotically Nonexpansive Mappings

在具一致正规结构的一致G-微分的实Banach空间E框架下,引入一种关于渐近非扩张映像T的新的迭代格式,并证明由此产生的迭代序列{xn}满足一定条件时,强收敛于T的不动点.其结果在更广的空间中把非扩张映像推广到了渐近非扩张映像,从而推广和改进了近代一些相关结果.

This paper introduces a new iterative process for asymptotically nonexpansive mappings on a real Banach space E with uniformly Gteaux differentiable norms.It is proved that the iterative sequence {xn} strongly converges to a fixed point of T under certain appropritate conditions.The results have improved and extended some recent results.