The Unique Existence Of Some Contractive Mapping Fixed Point In Partial B-metric Space

In 2013, Shukla proposed the concept of partial b-metric space on the basis of partial metric and b-metric, and studied the Banach contraction mapping principle in partial b-metric space.The partial b-metric space generalizes the general metric space, the research of the problem of nonlinear in partial b-metric space contributes important academic value and scientific significance to the enrichment and develop-ment the theory of nonlinear analysis.This paper mainly studied some fixed point problems of several kinds of mapping are proved by iterative approach in partial b-metric spaces. There are three chapters in this thesis.In chapter one, as an introduction, we recall the history and the current re-search status of the fixed point theorems in partial b-metric spaces, and also give a summary of this work.In chapter two,We introduced some related concepts of partial b-metric spaces ,the (δ, L)-weak contraction mappings and a new weak contraction mappings are defined and some new fixed point theorems for these type contraction mappings are proved in partial b-metric spaces.In chapter three,the generalized (ψ,ψ,f)-weak contraction mappings are de-fined and some new fixed point theorems for these type contraction mappings are proved by iterative approach in partial b-metric spaces.In chapter four,the Suzuki-type contraction mappings are defined and some new fixed point theorems for these type contraction mappings are proved in partial b-metric spaces.