Iterative Sequences To Fixed Point Of Nonexpansive Mapping

In recent years, the viscosity approximation methods for fixed points of nonexpansive mappings in Banach space setting have been discussed by many scholars. In chapter 1 of this thesis, the author explains the present condition of this question.In chapter 2 of this thesis, combining the previous articles, we discuss the iterative: where T a nonexpansive self-mapping of C with F(T)≠(?). A self-mapping f:C�'C is a contraction on C and there exists a constantα∈(0,1), f∈∏c, we can consider {αn),{βn} and {γn} being three real sequences in[0,1]. If {αn},{βn},{γn} andαsatisfy the certain conditions, we can use the viscosity approximation methods to get the strong convergence of {xn}.By using the viscosity approximation methods for fixed points of nonexpansive mappings in Banach space, we can reach the conclusions of the strong convergence for the iterative sequences. The results extend and improve the main results of Yao Yonghong and Chen Rudong.In chapter 3, the author is concerned with composite implicit iteration process: where T a nonexpansive self-mapping of C with F(T)≠(?). A self-mapping f:C�'C is a contraction on C,f∈∏c, there exists a constantα∈(0,1). Let {αn},{βn} be two real sequences in [0,1]. We can use the viscosity approximation methods to get the strong convergence if {αn},{βn} andαsatisfy the certain conditions.