| As a very significant problem in the filed of nonlinear functional analy-sis,split feasibility problem has been widely applied in radioactive therapy,image reconstruction and computed tomography and also been studied by many math-maticians.This problem can efficiently reflect the relationship of two sets by a bounded linear operator.But it is well known that many problems in real world are nonlinear,thus the bounded linear operator restrict the problem to some ex-tent.Thus changing the bounded linear operator to a nonlinear operator will be vital both in theory and applications.However,there is only little work studying nonlinear split feasibility problem up to now because of its level of difficultySo,in this thesis,the nonlinear operators in nonlinear split feasibility problem are found.And iteration algorithms by using fixed point method is constructed to approximate the solution of nonlinear split feasibility problem.In this case.nonlinear split feasibility problem is studied in infinite-mensional spaces.The following aspects will be discussed in this thesisFirstly,the background and current research state of split feasibility problem and nonlinear split feasibility problem are introduced,and the research interests are illustrated.Secondly,two kinds of nonlinear operators are introduced in Hilbert spaces In this case,the sufficient condition of the existence of nonlinear split feasibility problem is given.And an iteration algorithm is proposed and the theorem of convergence is proved.Besides,this problem is transferred to an equation problem in Banach spaces and solved by divided difference methodFinally,using the result of solving nonlinear split feasibility problem,the nonlinear split common fixed point problem is also solved as an application. |
