Iteration Methods Research On Nonexpansive Mappings And Pseudocontractive Mappings

Nonlinear functional analysis has deep connection with many branches in modern maths, especially in study of the existence and uniqueness of solutions to differential equations, integral equations, operator equations and approximation of iteration processes. Fixed point theories of nonlinear operators are the kernels of nonlinear functional analysis. In order to construct zeros for abstract operators in Banach spaces, there have been a lot of iteration processes. The convergence of iteration schemes is of importance in fixed point theories of nonlinear operators.Using geometric theories of Banach space and nonlinear operator theories, we work on fixed point properties of nonlinear operators on two fields: on the one hand, to explore extensively the operator properties;on the other hand,to construct effective iterative schemes to approximate to the fixed point. Some new convergence results for nonexpansive, pseudocontractive mappings and accretive operators have been established or generalized, which improve the previous known results.