| In this paper,we study the properties of soft metric space and the fixed point theorem of strong complete soft metric space.In Chapter 1,the concepts and basic operations of soft sets are introduced.It is clear that the soft sets are one-to-one corresponding to soft matrices,and we give a simple application of the soft matrix in a decision making problem from the perspective of elementary transformation.In Chapter 2,we introduce the soft function defined by Molodtsov in his paper[1],in order to understand the meaning of this soft function,we give a concrete example of it.Then we define the totally ordered parameter set and the Hausdorff metric between two soft sets.And then we prove some fixed point theorem of strong complete soft metric space by giving some conditions of F_m and the totally ordered parameter setE.In Chapter 3,we introduce the related concepts and operations of soft metric space,define the Cartesian product space of two soft metric spaces,and prove its completeness and sequence compactness.Because of the different of (?) and (?),we define the concept of strong Cauchy sequence,improved the conclusions of Mujahib et al..By defining functions (?) and the compatible metrics and,we obtain a new fixed point theorem and generalize it to two mappings.In the process of proof,the difference between the soft real constant (?) and the soft real number (?) leads to different contraction conditions and reflects the necessity of the strong Cauchy sequence. |
