The Research On Contractive Fixed Point Theorems In Two Types Of Spaces

By using Suzuki's lemma,two classes of fixed point theorems of implicit contraction containing six variable continuous functions are given in b-metric spaces.One of our results generalizes the theorems of Berinde et al.from metric spaces to b-metric spaces.Based on our results,we can obtain the Banach,Kannan and Chatterjea types of fixed point theorems in b-metric spaces.In particular,the corollary of Banach type is the result of Nguyen Van dung et al.,which is an answer to the questions of Jovanovic et al..The other one of our results unifies the contractive condition of two theorems in the setting of b-metric spaces,which were given by Karapinar et al.in metric spaces and Aydi et al.in rectangular metric spaces.On the other hand,in dislocated quasi metric spaces,a fixed point theorem for nonlinear cyclic ?-contractive mappings is established,which is the extension of fixed point theorem form metric spaces to dislocated quasi metric spaces.Finally,we give an application to support our result.