Study On Some Fixed Point Theorems In B-metric Spaces With Qt-functions

In this paper,we study several kinds of common fixed point problems in b-metric spaces with Qt-function.The following tasks are completed:1.We put forward the concept of Qt-function in b-metric space,which generalizes the concepts of wt-distance,w-distance and Q-function.Meanwhile,we establish the Geraghty type common fixed point theorem in b-metric space with Qt-function,which generalizes some Geraghty type fixed point theorems.In addition,the sufficient conditions for the existence of solutions of a class of integral equations are obtained by using our results.2.We establish the Ciric type common fixed point theorems in b-metric space with Qt-function,which removes the condition of the Fatou property in the result of Amini-Harandi.In addition,we establish the Ciric type common fixed point theorems for four mappings.3.We solve the open problem proposed by Radenovic et al.We have answered the ques-tion of Radenovic et al.by means of two counter examples.Meanwhile,we give sufficient conditions for the existence of fixed points of Ciric type cyclic mappings in b-metric space.