Fixed Point Theorems For Contractive Mappings On Several Generalized Metric Spaces

Fixed point theory is an important part of nonlinear functional analysis,It is widely used in solving algebraic equation,functional equation,differential equation and so on.In recent years,fixed point problem of metric space has attracted the attention of scholars in various fields and has been studied extensively by many scholars.In this paper,some new fixed points and common fixed point theorems in E-metric spaces,D~*-metric spaces with Banach algebras and cone b-metric spaces with Banach algebras are discussed.This paper is divided into four chapters.The first chapter mainly introduces the research background of fixed point theory and the research status at home and abroad.In chapter 2,we discuss the topological properties related to semi-interior points in E-metric spaces,obtain fixed point theorems of Hardy Rogers type contraction mapping in non-solid cones,and discuss the common fixed point theorems of weakly compatible mapping pairs in the spaces.Then,the concepts of quasi-contraction mapping and weak quasi-contraction mapping are introduced in E-metric spaces,and some new conclusions of fixed points are obtained.The third chapter discusses the fixed point theorem in D~*-metric space over Banach algebras with solid cones.Moreover,the concept of ?~*-admissible mapping is introduced in D~*-metric space,a fixed point theorem with an admissible mapping condition in the partial order D~*-metric space with Banach algebras is obtained.Then we discuss the common fixed point theorem in such space.In chapter 4,we discuss the fixed point theorem in cone b-metric space over Banach algebra,and discuss the mapping principle of Ciric contraction and quasi contraction in this space.