Research On Fixed Point Problem In S-metric Space

The fixed point theory and applications have always been one of the important research topics in the discipline of nonlinear functional analysis.Since Banach proposed the principle of contraction mapping,the research on fixed point theory has been favored by scholars at home and abroad.Fixed point theory has now become one of the active research fields of basic mathematics.Scholars have explored the fixed point problem of operators by studying different types of operator or generalizing the general metric space,and the results enriched fixed point theory.This thesis mainly investigates the existence and uniqueness of fixed point for different types of mapping in the-metric spaces and it is divided into four sections:The first chapter introduces the knowledge background and research significance of the fixed point field,describes the development status of the fixed point theory in-metric spaces,and then expounds the work arrangement.The second chapter,we explores the fixed point theorem that satisfies the S-contractive mapping in complete-metric spaces,By improving the weak F-compressed function condi-tion,we prove the existence and uniqueness of fixed points under this type of mapping.The third chapter,we introduces the concept of C^*-algebra and study the fixed point problems in the C^*-algebra-valued-metric spaces.Fixed point problems are exploed and some fixed point theorem are obtained by constructing contractive conditions.An applica-tion is proved the validity of theorems,and the results generalize and improve some relevant conclusions.The fourth chapter introduces the Hausdorff metric relative to-metric spaces based on the concept of multi-valued contractive mapping,the fixed point theorem for multi-valued(?-?)-weak contractive mapping is obtained by constructing contractive conditions.The results improve and extend some conclusions about the multivalued mapping fixed point.