Some Fixed Point Theorems Of Several Contraction Mappings In Quasi-partial B-metric Spaces And C*-algebra-valued B-metric Spaces

In 1993,Czerwik proposed the concept of b-metric spaces,then several mathe-maticians generalize the concept of b-metric spaces in partial b-metric spaces?quasi-partial b-metric spaces?C*-algebra-valued b-metric spaces and so on,also several fixed point theorems of contraction mappings are researched.In the paper,we introduce the concept of some quasi-partial b-metric spaces,C*-algebra-valued b-metric spaces,by using the method of iteration,we study some fixed point problems of several kinds of contraction mappings in those spaces,our results promote and improve the results of recent related articles.The paper is divided into five chapters:In chapter one,we mainly elaborate the background and the current research status of the fixed point theorems for quasi-partial b-metric spaces,C*-algebra-valued b-metric spaces,and also give a summary of this work.In chapter two,we introduce the some related concepts of quasi-partial b-metric spaces,the(?_tsp-?,?)contraction mapping and the generalized ?-v contraction mapping are defined and some fixed point theorems for these type contraction map-pings are proved under certain conditions in quasi-partial b-metric spaces.In chapter three,the ?-cyclic contraction mappings are defined in quasi-partial b-metric spaces and some new fixed point theorems for these type cyclic mappings are proved in quasi-partial b-metric spaces.In chapter four,we discuss the existence and uniqueness of fixed point theorems in C*-algebra-valued b-metric spaces by using generalized Banach contraction map-pings.Some new fixed point theorems are given,which largely improve and extend some relative results that have been published recently in this spaces.In chapter five,the Jungck-contraction mappings are defined in C*-algebra-valued b-metric spaces,and some new common fixed point theorems for this type contraction mappings are studied in C*-algebra-valued b-metric spaces.