Research On Some Nonlinear Mappings Problems In Generalized Metric Spaces

In this paper,under the several new contractive conditions,the fixed point theorems' problem of existence and uniqueness about nonlinear mappings are studied in PGM-space.We further discuss it in generalized metric spaces under the new expansive contraction and the process of some existing proof are simplified as well.In this paper,the results that we obtain are generalized to the results in recent articles.This thesis is divided into four chapters.Chapter 1,the research background and current situation are mainly introduced in the metric spaces and the generalized metric space about fixed point theorem,and we briefly describe the research significance of this article.In addition,at the end of this chapter,some concepts and conclusions which will be used in this paper are given.In chapter 2,a weaker contractive condition is led in and we study the fixed points' problems of existence and the uniqueness about mixed monotone mapping in PGM-space.In chapter 3,a new expansive contractive condition is introduced,and we establish the fixed point and common fixed point theorems in the partial metric space.In chapter 4,two new concepts of contractive mapping are given,and the fixed point problem of contractive mapping is studied in the b-metric-like space.