Iterative Approximation Of Fixed Points For Non-self Mappings

The theory of fixed point for non-self mappings is an important part of the theory of fixed point. Especially, in recent years, the problem of iterative approximation of fixed point for non-self mappings becomes a very popular subject. The problem of fixed point is one of the emphasis problems of people's regard and the corresponding research has gained many great achievements. Among many directions of the fixed point researches, it becomes a main problem at the convergence problem about making approximating fixed point sequence and its application in control, nonlinear operator and derivative equation etc. The research of this problem will play an important role in its application in reality.The problem of iterative approximation of fixed point for non-self mappings and strongly pseudo-contractive mappings is discussed in this paper. The paper contains four parts. The main results are as following:Firstly, the development of the fixed point theory home and abroad is narrated. The main content that we will discuss, background and significance are introduced.Secondly, in the real uniformly convex Banach space E, the problem of iterative approximation of common fixed point of multistep iterative process for non-self asymptotically nonexpansive mappings{T_i : i= 1,2,N} is discussed.Thirdly, the problem of iterative approximation of common fixed point of modified multistep iterative process for non-self asymptotically nonexpansive mappings{T_i : i= 1,2,N} is discussed.Finally, the Mann iterative scheme and the Mann iterative scheme with errors for non-self strongly pseudo-contractive mapping are introduced. In the real uniformly smooth Banach space, the problem of iterative approximation of fixed point of the above iterative for non-self strongly pseudo-contractive mapping{T_i : i= 1,2,N} are proved.