主要研究在巴拿赫空间中具误差的渐进伪压缩映射Ishikawa和Mann 迭代收敛到不动点的问题.Ishikawa迭代和Mann迭代是具误差的Ishikawa迭代和Mann迭代的特例.在以前的基础上,将渐进伪压缩映射从单值推广到多值,将Ishikawa迭代和Mann迭代从不带误差推广到带误差.论文中所得到的结果是对以前结果的一种推广.
Ishikawa-type and Mann-type iterative sequences of asymtotically pseudocontractive mappings with error mem ber were studied to converge to fixed points in Banach space.Ishikawa-type and Mann-type with errors scheme includes Ishikawa-type and Mann-type iterations as special cases. The results obtained in this paper represent an extension as well as refinement of previous known results.
[1] 张石生. Banach空间中渐近非扩张映象不动点的迭代逼近问题 [J]. 应用数学学报 2001.doi:10.3321/j.issn:0254-3079.2001.02.010
[2] Zhang Shisheng. Convergence problem for φ-pseudo-contractive mappings of Ishikawa-type and Mann-type iteration with an error member [J]. Applied Mathematics and Mechanics 2001, 21(01).
[3] SAHU D R. Strong convergence theorems for nonexpansive type and non-self multi-valued mappings [J]. Nonlinear Analysis-Theory Methods and Applications 1999, 37.
[4] JONG SOO JUNG, YEOL JE CHO, ZHOU HAIYUN. Iterative methods with mixed errors for perturbed m-accretive operator equations in arbitrary Banach spaces [J]. Mathematical and Computer Modelling 2002, 35.
[5] Xu Yuguang. Ishikawa and mann iterative processes with errors for non linear strongly accretive operator equation [J]. Mathematics Analysis and Applications 1998, 224.
[6] Chidume CE., Osilike MO.. Nonlinear accretive and pseudo-contractive operator equations in Banach spaces [J]. Nonlinear Analysis: An International Multidisciplinary Journal 1998, 7(7).