Fuzzy Contractive Mapping And Fixed Points In Fuzzy Metric Spaces

This paper mainly establishes a fuzzy metric spaces (Y, N,*),based on this new fuzzy metric spaces proof fuzzy contraction fixed point theory and interrupted time fuzzy contraction fixed point theory.This paper mainly have three parts:Firstly,it will introduce the new development of fuzzy sets and practical significance,research status and the application of fuzzy metric spaces in recent years,Many scholars have been corrected fuzzy metric space optimization.Secondly, in the many different views of currently available in fuzzy metric spaces, give a relatively new concept fuzzy metric spaces (Y,N,*),in the same time this paper gives the basic definition of N-Cauchy and P-Cauchy in fuzzy metric spaces (Y, N,*), and establishes a N-completeness of fuzzy metric spaces.In fuzzy metric spaces creates a new fuzzy contraction mapping.This paper uses the basic of iterative method,In fuzzy metric spaces proof fuzzy contraction mapping fixed-point existence and uniqueness. This paper give fuzzy contraction sequences necessary conditions for a unique fixed point in the N-completeness fuzzy metric spaces. And give an example to verify its feasibility.Finally,ti is when the proof of the following fuzzy metric space (YN,*) contraction mapping fixed point theorem,using the infinite product,defining the critical conditions for convergence.When the continuou time condition changed interrupted time proof fuzzy contraction mapping fixed-point theorey.And give an example to verify its feasibility.Then a brief introduction to the application of the theorem in the color image processing, image filtering technique that fuzzy metric. By comparing the results of different methods under color image processing, and further described in the color image processing fuzzy metric is a very good tool.The aim of this paper is to extend the Banach fixed-point theorem to contractive mappings on complete fuzzy metric spaces in several senses.