用修改的Ishikawa迭代序列逼近渐近非扩张映像的不动点

Approximating Fixed Points of Asymptotically Nonexpansive Mappings by Modified Ishikawa Iteration Process

研究了在一致凸Banach空间X中渐近非扩张映像T的不动点问题.运用分析技巧和分析方法,依据凸性模的连续性与单调性以及渐近非扩张映像的特征给出了一系列引理;通过对Ishikawa迭代序列中参数的适当控制,建立了修改的Ishikawa迭代序列{xn}强收敛到渐近非扩张映像T的不动点定理,该定理改进了相关文章的一些结论.

This paper investigates into the fixed points for asymptotically nonexpansive mappings in uniformly convex Banach X spaces. Employing some analytical skills and methods, it provides a series of lemmas in accordance with the monotony and continuity of the convexity’s modulus and the properties of asymptotically nonexpansive mappings. Moreover, it gives a convergence theorem, which shows that the modified Ishikawa iterative process ｛x_n｝ converges strongly to the fixed points of asymptotically nonexpansive mappings. The result presented improves related results in other papers.