The Fixed-point And Eigenvector's Problems Of Two Classes Of Nonlinear Operators

In this thesis, some existence problems of 1-set-contractive mapping's fixed points, eigenvalues and eigenvectors are discussed firstly. Then some problems of a class of 1-submixed monotone operators with convexity and concavity are investigated. This thesis consists of three chapters. And each chapter is an integrated paper.In chapter l,some properties of 1-set-contractive mapping's degree in W.V.Petryshyn [5] are used to discuss some existence problems of 1-set-contractive mapping's eigenvalues and eigenvectors. Some existence theorems of 1-set-contractive mapping's eigenvalues and eigenvectors are obtained and these are all new ones.In chapter 2,some properties of 1-set-contractive mapping's degree in W.V.Petryshyn [5] are also used, we have acquired some existence theorems of fixed points of 1-set-contractive mappings satisfying condition (c) in different edge conditions, which was mentioned in W.V.Petryshyn [9].These results are some important generalizations of Altman theorems in [8].Chapter 3 is devoted to a class of nonlinear operators with convexity and concavity. Using monotone iterative method, some existence theorems of fixed points are concluded without any hypothesis of continuity and compactness.