Generalized KM Iterative Algorithm And Its Application To Zero Point Problem And Splitting Feasibility Problem

Fixed point problem has a wide range of application in real life,and it is also a hot issue of current research.The classical KM iterative algorithm is an effective algorithm to solve the fixed point problem and it converges weakly in Banach spaces.Recently,Kanzow and Shehu proposed a generalized KM iterative algorithm in Hilbert spaces and proved its weak convergence.Based on the result of Kanzow and Shehu,this dissertation proves the weak convergence of the generalized KM iterative algorithm in Banach spaces and applies it to zero point problem;also we put forward the variable generalized KM iterative algorithm in Banach spaces.With the help of the previous research methods,we prove its weak convergence and apply it to splitting feasibility problem.In the first chapter,the research background and significance of the generalized KM iterative algorithm are explained,as well as the arrangement of this dissertation.In the second chapter,we introduce some basic knowledge and lemmas needed in this dissertation,and prove a vital lemma.In the third chapter,we first prove the weak convergence of the generalized KM algorithm in Banach spaces,and give examples to show that the existence of the real number sequence satisfying the condition of the theorem.Secondly,variable generalized KM algorithm is put forward and we prove its weak convergence under suitable assumptions in Banach spaces.In the fourth chapter,the generalized KM algorithm and the variable generalized KM algorithm are applied to zero point problem and split feasible problem respectively.In the fifth chapter,we summarize the whole dissertation and put forward the future research direction.