The Unique Existence Of Some Contractive Mapping Common Fixed Point In G_pb-metric Space

In 2011,Zand and Nezhad proposed the concept of Gp-metric space on the basis of G-metric and p-metric,and In 2013,Aghajani,Abbas and Roshan proposed the concept of Gb-metric space on the basis of G-metric and b-metric.In this paper,we define a Gpb-metric space which is based on the Gp-metric and Gb-metric.Gpb-metric space is in the form of three dimensional partial b-metric space and it generalizes the general metric space to a great degree,so the research of the problem of nonlinear in it contributes important academic value and scientific significance to the enrichment and development of the nonlinear analysis.In this paper,by using the method of iteration,we study some common fixed point problems of several kinds of contraction mapping in Gpb-metric space.The paper is divided into four chapters:In chapter one,we mainly elaborate the background and the current research status of the fixed point theorems for Gpb-metric space,and also give a summary of this work.In chapter two,We mainly define the Gpb-metric space and some related con-cepts of it,the(?,L)-weak contraction mappings are defined and some new common fixed point theorems for this type of contraction mapping are proved under certain conditions in Gpb-metric space.In chapter three,the(?,?)-weak contraction mappings and the generalized(?,?)-weak contraction mappings are defined and some common new fixed point theorems for these type contraction mappings are proved under certain conditions in Gpb-metric space.In chapter four,the F-implicit contractive mappings are defined and some new common fixed point theorems for this type contraction mappings are proved under certain conditions in Gpb-metric space.