Fixed Point Theory And Some Applications Of Several Classes Of Nonlinear Operators

In this thesis, we study the existence of fixed points of several classes of operators by making use of partial order method,and set up several new theorems of fixed point. The full thesis divides into six chapters.In chapter one, we introduce some basic important knowledge which will be used in the latter chapters of thesis. In chapter two, we define the concept of order non-expansive operator, and investigate the fixed-point existence problem, obtained some fixed-point theorems. In chapter three, the existence of fixed point for some class of non-compact decreasing operators is studied, some existence and uniqueness theorems are obtained, finally, we give an example of application.In chapter four, we discuss mixed monotone operator and get several theorems under non-compact continue. In chapter five, we define a new partial order ( -partial order) in Hilbert space, by the new partial order we construct several cones and discuss properties of the cone, finally, we get some fixed point theorem. In chapter six, we apply -partial order into designing a new kind of sequence cryptography. tt...