Some Fixed Point Theorems Of Several Contraction Mappings In B-metric Space

In 1993,Czerwink proposed the concept of b-metric space,In 1994,Matthews proposed the concept of partial metric space,and in 2013,Shukla define a partial b-metric space which is based on the b-metric and partial metric.The b-metric space and partial b-metric space generalizes the metric space in the general sense,so the researches of the problems of nonlinear in them contribute 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 mappings in b-metric space and partial b-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 b-metric space and partial b-metric space,and also give a summary of this work.In chapter two,the almost generalized C-contractive mappings are introduced into the ordered b-metric space,and the existence and uniqueness of fixed points and common fixed points in the ordered b-metric spaces are proved respectively.Finally,give an example to support this conclusion.In chapter three,the(?,?,?,?)-contractive multi-valued mappings are defined and the existence of fixed points for this type contraction mappings are proved under certain conditions in ?-complete b-metric space.In chapter four,the existence and uniqueness of coupling coincidence points satisfying some contractive conditions are proved in the partial b-metric space,and when F,g are ?-compatible mappings,the existence of common coupling fixed points is proved.