【作者】 蔡钢；

【导师】 胡长松；

【作者基本信息】 湖北师范学院 ， 应用数学， 2010， 硕士

【摘要】 非线性算子不动点理论和均衡理论是非线性泛函分析的重要组成部分,尤其是非线性算子方程解的迭代逼近问题已成为非线性泛函分析领域近年来研究的活跃课题.该文对严格伪压缩映象的不动点问题和均衡问题进行深入研究,建立了更有效的迭代过程来逼近一族严格伪压缩映象的公共不动点集的公共元和一族严格伪压缩映象的公共不动点集与均衡问题解集的公共元,所得结果改进和推广了许多作者的最新结果.全文共分四章.第一章介绍了非线性算子理论及迭代算法的背景及本文的主要工作.第二章在q一致光滑Banach空间框架下讨论了无限个λi-严格伪压缩自映象的带误差的修改的Ishikawa迭代过程的强收敛问题.第三章在q一致光滑Banach空间框架下讨论了有限个λi-严格伪压缩非自映象的一般迭代过程的收敛性问题.第四章在Hilbert空间框架下讨论了找有限个依中间意义的渐进ki-严格伪压缩映象的公共不动点集和均衡问题解集的公共元问题.更多还原

【Abstract】 The fixed point theory of nonlinear operations and equilibrium problems are important parts of nonlinear functional analysis. Especially, the problem of approximating to solutions of nonlinear operator equations becomes the topic that people study in the recently years. In this paper, we construct effective schemes to approximate the common fixed point of a family ofλi—strictly pseudocontractive mappings and find a common element of the set of common fixed points of a finite family of asymptotically ki—strictly pseudo-contractions in the intermediate sense and the set of solutions of an equilibrium problem. Results presented in this paper improve and extend many authors’recent results. This paper includes fives chapters. Now we will describe them briefly one by one.Chapter 1 recalls the history and present situation of nonlinear operator equations in Banach spaces and we also give a summary of this work.Chapter 2 mainly concerns about the convergence problems of modified Ishikawa iter-ative process with errors for an infinite family of strict pseudocontractions in q—uniformly smooth Banach spaces.Chapter 3 mainly discusses about the convergence problems of a general iterative pro-cess for a finite family ofλi—strict pseudocontractions in q—uniformly smooth Banach spaces.Chapter 4 mainly considers convergence analysis for equilibrium problems and fixed point problems of a finite family of asymptotically ki—strictly pseudocontractive mappings in the intermediate sense in Hilbert spaces.更多还原