关于修正的Ishikawa迭代序列的稳定性和收敛性

Stability and convergence of modified Ishikawa iterative sequences

关于严格渐近伪压缩映象和渐近伪压缩映象具平均误差的修正的Ishikawa和修正的Mann迭代序列的收敛性和稳定性之间的等价性问题的研究,一般都是在D有界或在序列{xn}与{Tnxn}有界的条件下进行研究的。而D有界或{xn}与{Tnxn}有界性条件,在一定程度上限制了某些研究成果的使用。笔者的目的是在取消{xn}与{Tnxn}有界的条件下,并用更弱条件γn→0(n→∞)取代γn=o(αn),使用新的分析技巧,在实Banach空间中建立了依中间意义渐近非扩张的严格渐近伪压缩映象和渐近伪压缩映象具平均误差的修正的Mann和Ishikawa迭代序列收敛性和稳定性之间的等价性的充分必要条件。由于在去掉{xn}与{Tnxn}有界性的条件时,并没有增加其他条件,因此笔者的结果,本质上改进和推广了有关文献中的相应结果。

It is a study about equivalence theorems between convergence and stability of modified Ishikawa and modified Mann iterative sequences with mean errors for strictly asymptotically pseudocontractive mappings and asymptotically pseudo-contractive mappings in Banach spaces.It is generally about the study under the conditions of D or {xn} and {Tnxn} boundedness,while D or {xn} and {Tnxn} boundedness conditions,restricts the use of some study results to a certain extent.The purpose of this paper is to establish some sufficient and necessary conditions on some equivalence theorems between convergence and stability of modified Ishikawa and modified Mann iterative sequences with mean errors for strictly asymptotically pseudocontractive mappings and asymptotically pseudocontractive mappings with asymptotically nonexpanisive mappings in the intermediate senseunder the condition of removing the restriction bounder {Tnxn} and {xn},and substituente γn=o（αn） with the weaker condition γn→0（n→∞） in Banach spaces by using a new analytical method.Due to removed {xn} and {Tnxn} boundedness conditions,and no increase in other conditions,so our results essentially extend and improve the corresponding results in some references.