Research On Fixed Points Of Contractive Mappings In Two Classes Of Generalized Metric Spaces

Fixed point theory is an important part of nonlinear functional analysis.Many mathematical problems can often be transformed into solving prob-lems of algebraic equations,functional equations,differential equations,etc.and then solved by using fixed point theory.In recent years,the existence and uniqueness of the fixed points of self-mapping on generalized metric spaces have been attentioned by many people,a lot of researches have been done on various contractive mappings,and many results have been obtained.In this thesis,the existence and uniqueness of fixed points of fuzzy Meir-Keeler type contractive mappings on complete fuzzy metric spaces and Meir-Keeler type contractive mappings,θ-φ type contractive mappings,andθ-φ Chatterjea-type contractive mappings on complete partial b-metric s-paces are discussed.It consists of four chapters:In Chapter 1,the historic background,the current situation and develop-ment trend of the fixed point theory are introduced.In Chapter 2,a kind of fuzzy Meir-Keeler type contractive mappings are introduced,the existence and uniqueness of the fixed point of the fuzzy Meir-Keeler type contractive mappings on complete fuzzy metric spaces are discussed,and a fuzzy ψ-contractive mapping is a fuzzy Meir-Keeler con-tractive mapping is proved.In Chapter 3,a kind of Meir-Keeler type contractive mappings on the complete partial b-metric spaces are introduced,the existence and unique-ness of the fixed point of the Meir-Keeler type contractive mapping on the complete partial b-metric spaces are discussed.In Chapter 4,a kind of θ-φ type contractive mappings and a kind of θ-φ Chatterjea-type contractive mapping are introduced,the θ-φ type contractive mapping and the θ-φ Chatterjea-type contractive mapping on the complete partial b-metric spaces are studied,and the existence and u-niqueness conditions of the fixed points of these two types of contractive mappings are obtained.