2-度量空间上满足隐式条件的两个映射的公共不动点
发布时间：2018-09-04 13:15
【摘要】：Banach不动点定理是不动点理论中最基本的理论之一.并且它在数学与其他领域中具有广泛的应用.许多学者们推广和改进了 Banach不动点定理,特别是在2-度量空间得到的一些重要的关于不动点、公共不动点、重合点的存在性结论.在Banach不动点理论的发展中,有几个较为典型的定理.比如,Geraghty不动点定理,Kannan不动点定理,Chatterjea不动点定理,积分不动点定理及一些变形和推广结果.本文,首先引入称之为Geraghty函数的一类函数,并结合Kannan和Chatterjea收缩条件,考虑并得到2-度量空间上满足Geraghty-kannan型及Geraghty-chatterjea型收缩条件的两个映射的公共不动点存在定理.这两个结论是Geraghty-Banach定理的扩展结果.其次通过引入若干的实函数,建立具有积分型的隐式收缩条件,并给出满足此条件的两个映射具有唯一公共不动点的结果。本文所得结果很好地推广和改进了一些已知结果,并指出了如何把实度量上的结论推广到2-度量空间的一种方法和思路.
[Abstract]:Banach Fixed Point Theorem is one of the most basic theories in fixed point theory, and it is widely used in mathematics and other fields. Many scholars generalize and improve Banach Fixed Point Theorem, especially some important conclusions about the existence of fixed points, common fixed points and coincidence points in 2-metric spaces. For example, Geraghty fixed point theorem, Kannan fixed point theorem, Chatterjea fixed point theorem, integral fixed point theorem and some deformation and generalization results. In this paper, we first introduce a class of functions called Geraghty functions, and consider and combine Kannan and Chatterjea contraction conditions. The existence theorems of common fixed points for two mappings satisfying the contraction conditions of Geraghty-kannan type and Geraghty-chatterjea type on 2-metric spaces are obtained. These two results are the extended results of Geraghty-Banach theorem. Secondly, by introducing some real functions, the implicit contraction conditions with integral type are established, and two implicit contraction conditions satisfying these conditions are given. The results obtained in this paper extend and improve some known results well, and point out a method and train of thought of how to extend the conclusion of real metric to 2-metric space.
【学位授予单位】：延边大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177.91
本文编号：2222212
[Abstract]:Banach Fixed Point Theorem is one of the most basic theories in fixed point theory, and it is widely used in mathematics and other fields. Many scholars generalize and improve Banach Fixed Point Theorem, especially some important conclusions about the existence of fixed points, common fixed points and coincidence points in 2-metric spaces. For example, Geraghty fixed point theorem, Kannan fixed point theorem, Chatterjea fixed point theorem, integral fixed point theorem and some deformation and generalization results. In this paper, we first introduce a class of functions called Geraghty functions, and consider and combine Kannan and Chatterjea contraction conditions. The existence theorems of common fixed points for two mappings satisfying the contraction conditions of Geraghty-kannan type and Geraghty-chatterjea type on 2-metric spaces are obtained. These two results are the extended results of Geraghty-Banach theorem. Secondly, by introducing some real functions, the implicit contraction conditions with integral type are established, and two implicit contraction conditions satisfying these conditions are given. The results obtained in this paper extend and improve some known results well, and point out a method and train of thought of how to extend the conclusion of real metric to 2-metric space.
【学位授予单位】：延边大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177.91
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