一些映象不动点定理与迭代序列收敛性

发布时间：2018-06-27 07:17

  本文选题：模糊度量空间 + Φ-压缩映象　； 参考：《渤海大学》2017年硕士论文

【摘要】：本文首先在完备的模糊度量空间中建立了两类Φ-压缩映象的一些不动点定理,并使用模糊度量空间Φ-压缩映象不动点定理讨论了起源于动态规划的一类泛函方程解的存在与唯一性.同时在轨道完备度量空间中研究Ciric-Altman型映象不动点和带有对称函数的非唯一不动点的存在性,证明了几个新的不动点定理.其次在实赋范线性空间研究渐近伪压缩型映象的迭代序列收敛性问题,在较弱条件下建立了有限族渐近伪压缩型映象不动点具有误差的迭代序列的强收敛定理,同时也给出几个例子说明本文结果的有效性与广泛性.然后使用新的分析方法,在实赋范线性空间研究广义渐近S-半压缩型映象的迭代序列收敛性问题,在较弱条件下建立了有限族广义渐近S-半压缩型映象不动点具有误差的迭代序列的强收敛定理.最后在实Banach空间中研究了Lipschitz的k-次增生算子方程x+Tx=f解的带误差的迭代序列收敛性与稳定性问题,并给出了新的收敛率的估计式,从而推广和改进了有关文献中的相应结果.
[Abstract]:In this paper, we first establish some fixed point theorems for two classes of 桅 -contractive mappings in complete fuzzy metric spaces. By using the fixed point theorem of 桅 -contractive mapping in fuzzy metric space, the existence and uniqueness of solutions for a class of functional equations originating from dynamic programming are discussed. At the same time, we study the existence of fixed points for Ciric-Altman type mappings and non-unique fixed points with symmetric functions in orbital complete metric spaces, and prove some new fixed point theorems. Secondly, the convergence problem of iterative sequences for asymptotically pseudo-contractive type mappings is studied in real normed linear spaces. Under weaker conditions, the strong convergence theorems for iterative sequences with fixed points with errors for finite families of asymptotically pseudo-contractive type mappings are established. At the same time, several examples are given to illustrate the validity and extensibility of the results. Then the iterative sequence convergence problem of generalized asymptotically S-semicontractive type mappings is studied in real normed linear spaces by using a new analytical method. A strong convergence theorem for iterative sequences with errors of fixed points for generalized asymptotically S- semicontractive type mappings of finite families is established under weaker conditions. Finally, the convergence and stability of iterative sequences with errors for Lipschitz's k- subaccretive operator equation x T _ XF are studied in real Banach spaces, and a new estimate of convergence rate is given, which generalizes and improves the corresponding results in relevant literatures.
【学位授予单位】：渤海大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177.91

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