Research On Some Coupled Common Fixed Point Problems In G-metric Spaces

In rercent years, the research on the coupled common fixed theory and application have become hot issue in nonlinear analysis, and have been attentioned by some scholors. Some scholors achieved some good results. It is applied to many different fields such as differential equations, integral equations, variational inequalities, optimization theory and fuzzy mathematics and so on. So the research of the coupled commom fixed point make it more theoretical significance and application value in nonlinear analysis.This paper mainly studied some coupled common fixed point theorems in partially oredered G-metric spaces. There are three chapters in this thesis.In chapter one, the historical backgrounds and current situation of G-metric space theory and application are introduced and some related concepts of G-metric spaces are given in an introductory.In chapter two, this part, firstly, discussed some coupled common fixed point theorems for compatible mappings in partially oredered G-metric spaces and secondly, researched some coupled common fixed point theorems for(,)ga j-contr-active mappings in partially oredered G-metric spaces. Simultaneously, we give some examples to illustrate the significance of our main results. And these results generalize the existing related conclusions.In chapter three, a new(f,y) conditions of mappings are proposed in the partially ordered G-metric spaces and some quadruple fixed point theorems are achieved under the(f,y)-contractive condition. Simultaneously, we give an example to illustrate the significance of our main results. And these results generalize the existing related conclusions.