本文選題：模糊度量空間 + Φ-壓縮映象��； 參考：《渤海大學(xué)》2017年碩士論文

【摘要】：本文首先在完備的模糊度量空間中建立了兩類Φ-壓縮映象的一些不動(dòng)點(diǎn)定理,并使用模糊度量空間Φ-壓縮映象不動(dòng)點(diǎn)定理討論了起源于動(dòng)態(tài)規(guī)劃的一類泛函方程解的存在與唯一性.同時(shí)在軌道完備度量空間中研究Ciric-Altman型映象不動(dòng)點(diǎn)和帶有對(duì)稱函數(shù)的非唯一不動(dòng)點(diǎn)的存在性,證明了幾個(gè)新的不動(dòng)點(diǎn)定理.其次在實(shí)賦范線性空間研究漸近偽壓縮型映象的迭代序列收斂性問(wèn)題,在較弱條件下建立了有限族漸近偽壓縮型映象不動(dòng)點(diǎn)具有誤差的迭代序列的強(qiáng)收斂定理,同時(shí)也給出幾個(gè)例子說(shuō)明本文結(jié)果的有效性與廣泛性.然后使用新的分析方法,在實(shí)賦范線性空間研究廣義漸近S-半壓縮型映象的迭代序列收斂性問(wèn)題,在較弱條件下建立了有限族廣義漸近S-半壓縮型映象不動(dòng)點(diǎn)具有誤差的迭代序列的強(qiáng)收斂定理.最后在實(shí)Banach空間中研究了Lipschitz的k-次增生算子方程x+Tx=f解的帶誤差的迭代序列收斂性與穩(wěn)定性問(wèn)題,并給出了新的收斂率的估計(jì)式,從而推廣和改進(jìn)了有關(guān)文獻(xiàn)中的相應(yīng)結(jié)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.
【學(xué)位授予單位】：渤海大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O177.91

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