| Nonlinear analysis is an important research direction of modern mathematics. The fixed point theory of nonlinear operator, as a hot field of nonlinear functional analysis, has been drawing more and more attention by the scholars. Some good results have been proved and applied widely in economics, management science, and biology and engineering systems, where exist a large number of nonlinear problems. Therefore, the research of fixed point theory in generalized metric spaces contributes important academic value and scientific significance to the enrichment and development of nonlinear operator in both its theoretical and application.This paper mainly studies on the fixed point theorems of nonlinear operators in cone metric spaces and b- metric spaces. This thesis is divided into three chapters.In chapter one, the historical backgrounds and current situation of cone metric spaces and b- metric spaces on theory and application are introduced and some related concepts of cone metric spaces and b- metric spaces are given in an introductory.In chapter two, we get the common fixed point theorems for two pairs of non-selfmappings in cone metric space, and illustrate the effectiveness of the result. These results generalize and extend some related results.In chapter three,(s, r)-contractive multivalued operator is proposed. We get the fixed point theorems of(s, r)-contractive multivalued operator in b- metric spaces and illustrate the effectiveness of the result, and give an application to solve the integral equations. |
