Fixed Points Of Several Kinds Of Soft Contract Mappings In Soft Complete Metric Spaces

Banach contraction principle is one of the basic and the most widely applied fixed point theorem.On the basis of the soft set,this article makes several kinds of generalizations on the Banach contraction principle,several new contraction conditions and fixed point theorems are discussed.The full text is divided into five chapters.In the second chapter,the concept of soft set,soft element and its related operations are introduced,and the properties of soft metric and soft complete metric space are also introduced.Then the concept of soft linear space,soft norm and their properties are introduced,which can be used as a paving for later discussion.In the third chapter,we define the concepts of soft F contraction and soft F weak contraction,and also define some new concepts such as soft ? type F contraction and soft ? type F weak contraction.Some properties of these new contractions in soft complete metric spaces are discussed,and the fixed point theorems under these different contraction conditions are proved respectively.The fourth chapter is divided into two parts.The first part defines the concept of a new norm.Based on that,we study the properties of soft normed linear space and soft Banach space.The second part defines the soft uniformly convex Banach space.There also defines the concept of soft cyclic contraction and soft tricyclic contraction,and discusses the existence of the best proximity point.The fifth chapter,as a generalization of Meir-Keeler contraction mapping,defines soft quasi metric space from soft metric space,also introduces some new concepts such as the soft triangular (?) compatible mapping and soft (?) compatible Meir-Keeler contraction mapping.There also defines other generalized forms of the soft (?) compatible M-K contraction,and then discussed the fixed point problems.