节点文献
完备度量空间中不动点迭代序列强收敛性定理和公共不动点存在性定理
Strong Convergence Theorems and Common Fixed Points Theorems in Complete Metric Spaces
【作者】 王莹;
【导师】 邓磊;
【作者基本信息】 西南大学 , 应用数学, 2013, 硕士
【摘要】 本文主要研究Hilbert空间中渐近非扩张映射的不动点的迭代序列问题,完备度量空间中满足特定条件的弱压缩映射的不动点存在性问题和公共耦合不动点存在性问题,全文共分四部分:第一章,介绍了不动点理论的背景、本文的主要工作及意义.第二章,在Hilbert空间中对两个有限渐近非扩张映射族引入一个新的修正的Mann迭代序列,并证明该迭代序列强收敛于这两个有限渐近非扩张映射族的公共不动点.这些结果推广了一些Hilbert空间中关于渐近非扩张映射的不动点迭代序列的结论.第三章,在完备的度量空间中建立满足广义φ-弱压缩条件的两个集值映射的公共端点定理.推广了近来一些满足特定压缩条件的单值或多值映射的不动点结论.第四章,在完备的偏序度量空间中引入(φ,φ)-g-弱压缩条件,在此基础上得到满足该广义弱压缩条件的映射F:X×X→X和g:X→X的公共耦合不动点的存在性定理.这些结果推广了近来一些完备偏序度量空间中关于耦合不动点的结论.
【Abstract】 The problem of iteration sequence of fixed point in Hilbert space, the problem of existence of common fixed point and coupled coincidence fixed point for weak contractive mappings which satisfying certain conditions in complete metric space are discussed. The paper contains four parts as follows:In chapter one, the background of fixed point theory, main contents that we will discuss and significance are introduced.In chapter two, a new modified Mann’s iteration sequence for two finite families of asymptotically non-expansive mappings in Hilbert space is introduced. And we prove the iteration sequence converges strongly to a common fixed point of the two finite families of asymptotically non-expansive mappings in a Hilbert space. The presented theorems are generalizations of related conclusions of iteration sequences.In chapter three, common end point theorem is established for two multi-valued mappings which satisfy generalized φ-weak contractive conditions. Presented theo-rems generalized some fixed point results for single or multi-valued mappings which satisfy certain contractive factors.In chapter four, the concept of (ψ,φ)-g-weakly contractive mapping is intro-duced and four coupled coincidence point theorems for such mappings are established in an partially ordered complete metric spaces. Presented theorems are generaliza-tions of the recent coincidence fixed point theorems.
【Key words】 common fixed point; generalized weak contractive condition; exis-tence problem; iteration sequence; complete metric space; Hilbert space;