【作者】 吴智宇；

【导师】 胡长松；

【作者基本信息】 湖北师范学院 ， 应用数学， 2012， 硕士

【摘要】 本文讨论了一些非线性算子迭代方法的等价性问题以及有限个严格伪压缩映射的收敛定理,全文分为四章,摘要如下：第一章为绪论,介绍了非线性算子迭代方法以及不动点定理的实际意义、研究现状及本文所用到的相关知识和本文的创新之处.第二章主要研究了新的Ishikswa-Halpern迭代与粘性迭代方法之间的等价性问题,这里最主要把Meir-Keeler压缩映射(简称为MKC)这种算子融入到粘性迭代算法中第三章主要研究了在Bananch空间中一族有限个λi—严格伪压缩映射的收敛的定理。最后,在第四章对本文进行了总结和展望,并指出作为进一步研究的某些课题.更多还原

【Abstract】 The paper mainly studies the equivalence of some nonlinear iterations and the conver-gence theorems of finite nonexpansive mappings.The paper includes four chapters.The first chapter as an introduction, modeling process of nonlinear iterations and theconvergence theorems of fixed points, its real meaning, the current research status and themain work of this paper are addressed.In the second chapter,it is to establish some groups of equivalent theorems of conver-gence between modified Ishikswa-Halpern iteration and viscosity approximation method.Inthis chapter,it considers the viscosity approximation method with Meir-Keeler contrac-tion(MKC, for short)In the third chapter,we consider the convergence theorems of finite λi strictly pseudo-contractive mappings in Banach space.Finally, the conclusion is showed in the fourth chapter, and some problems we needstudy later are given.更多还原