The Research Of Fixed Point Theorem On B-metric Space

The research of the fixed point principle have a long time.From S.Banach formulated and proved contraction mapping principle,the fixed point theorems have been generalized to complete b-metric space by S.Czerwik,S.Nadler et al.In this paper,we discuss the fixed point theorems in b-metric space and obtains the corresponding results with wt-distance.In the first chapter,it introduces the research content of this paper,the development status of fixed point principle,mainly including the proposition of fixed point principle in metric space,the research results of different scholars in b-metric space,and introduced the research method of this paper.In the second chapter,we introduce some basic definitions of b-metric space,wt-distance and lemmas,and we prove the conditions that Cauchy sequence convergence.According to the hypothesis,we get the g-contractive fixed point theorem and(?,(?))-weakly contractive fixed point theorem in complete b-metric space with wt-distance.A sequence is constructed and its convergence is proved.The existence and the uniqueness of fixed points in a complete b-metric space is obtained by the lemmas and conditions.If the condition of wt-distance is symmetric,then the relevant inference is obtainedIn the third chapter,the condition of f and g are b-compatible mappings in b-metric space are defined,and prove the common fixed point theorem of four continuous mappings of wt-distance in complete b-metric space by the lemma of convergence of Cauchy sequence.When the wt-distance is symmetric,the relevant corollaries are obtained by removing the continuity of mapping.