本文選題：一致空間 + 類擬b-距離空間��； 參考：《內(nèi)蒙古大學(xué)》2017年碩士論文

【摘要】：不動點(diǎn)定理在數(shù)學(xué)的許多分支中都有著廣泛的應(yīng)用,本文主要在一致空間和類擬b-距離空間中討論非線性擬壓縮映射不動點(diǎn)定理的推廣和應(yīng)用.具體完成工作如下:1.在一致空間中,引入了推廣的q-距離(特殊地,推廣的p-距離)以及相對于推廣q-距離序列完備等概念.通過運(yùn)用推廣的q-距離和新的完備性,在一致空間中建立了滿足(φ,Ψ,p)-弱壓縮映射的不動點(diǎn)定理.這個定理推廣了 2013年Lakzian等人的結(jié)果.2.在類擬bb-距離空間中引入了一類(?)iri(?)型非線性擬壓縮映射的概念,并且建立了含有此類映射的公共不動點(diǎn)定理.這個結(jié)果將He等人在類擬距離空間中的一個結(jié)果推廣到類擬b-距離空間.同時,也獲得Amini-Harandi在6-距離中的結(jié)果,其中Fatou性質(zhì)的條件可以省去.作為應(yīng)用,我們給出了擬偏6-距離空間中的(?)iri(?)型公共不動點(diǎn)定理.3.2015年,Singh等人在完備的距離空間中給出了單個映射的推廣Suzuki型不動點(diǎn)定理.這個結(jié)果同時推廣了 Doric,Zhang等人的結(jié)果,并且他們提出一個關(guān)于兩個映射的公共不動點(diǎn)的猜想,我們證明了這一猜想并且回答了他們的問題。
[Abstract]:Fixed point theorems are widely used in many branches of mathematics. In this paper, we discuss the extension and application of fixed point theorems for nonlinear quasi-contractive mappings in uniform spaces and quasi-b-distance spaces. The details of the work are as follows: 1. In this paper, we introduce the concepts of generalized q-distance (special, generalized p-distance) and completeness of q-distance sequence relative to generalized q-distance in uniform space. By using the generalized q-distance and the new completeness, a fixed point theorem satisfying (蠁, 蠄 ~ (?) p ~ (+) -weakly contractive mappings is established in the uniform space. This theorem extends Lakzian et al.'s results. In this paper, we introduce a class of Irius in quasi-bb-metric spaces. The concept of nonlinear quasi-contractive mappings is presented, and the common fixed point theorems are established. This result extends a result of he et al in quasi-metric spaces to quasi-b-metric spaces. At the same time, the results of Amini-Harandi in 6-distance are obtained, in which the condition of Fatou property can be omitted. As an application, we give the pseudo-partial 6-metric space. In this paper, we give a generalized Suzuki fixed point theorem for a single mapping in a complete metric space. This result also generalizes Doricon Zhang's results and they present a conjecture on the common fixed points of two mappings. We prove this conjecture and answer their questions.
【學(xué)位授予單位】：內(nèi)蒙古大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O177.91

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

1 Jing Hui QIU;Fei HE;;A General Vectorial Ekeland's Variational Principle with a P-distance[J];Acta Mathematica Sinica;2013年09期

2 Jing Hui QIU;Fei HE;;P-Distances, Q-Distances and a Generalized Ekeland's Variational Principle in Uniform Spaces[J];Acta Mathematica Sinica;2012年02期

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本文編號：2020490