几类非线性压缩不动点定理的推广

发布时间：2018-06-15 03:49

本文选题：一致空间 + 类拟b-距离空间　；参考：《内蒙古大学》2017年硕士论文

【摘要】：不动点定理在数学的许多分支中都有着广泛的应用,本文主要在一致空间和类拟b-距离空间中讨论非线性拟压缩映射不动点定理的推广和应用.具体完成工作如下:1.在一致空间中,引入了推广的q-距离(特殊地,推广的p-距离)以及相对于推广q-距离序列完备等概念.通过运用推广的q-距离和新的完备性,在一致空间中建立了满足(φ,Ψ,p)-弱压缩映射的不动点定理.这个定理推广了 2013年Lakzian等人的结果.2.在类拟bb-距离空间中引入了一类(?)iri(?)型非线性拟压缩映射的概念,并且建立了含有此类映射的公共不动点定理.这个结果将He等人在类拟距离空间中的一个结果推广到类拟b-距离空间.同时,也获得Amini-Harandi在6-距离中的结果,其中Fatou性质的条件可以省去.作为应用,我们给出了拟偏6-距离空间中的(?)iri(?)型公共不动点定理.3.2015年,Singh等人在完备的距离空间中给出了单个映射的推广Suzuki型不动点定理.这个结果同时推广了 Doric,Zhang等人的结果,并且他们提出一个关于两个映射的公共不动点的猜想,我们证明了这一猜想并且回答了他们的问题。
[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.
【学位授予单位】：内蒙古大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177.91

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