Research On Iterative Algorithm For Fixed Point Of A Class Of Nonexpansive Operators

The fixed point theory is widely used in transportation,management,production and other practical problems.It is of great significance to construct an appropriate iterative algorithm to solve the fixed point problem under the practical background.Among many iterative algorithms,Krasnoselskii-Mann(KM)iterative algorithm is the most commonly used and has remarkable effect.Therefore,this paper carries out an in-depth study on KM iterative algorithm.First,in order to further generalize the weak convergence results of the generalized KM iterative algorithm and the variable generalized KM iterative algorithm in uniformly convex Banach space,this paper proves the strong convergence of the generalized KM iterative algorithm and the variable generalized KM iterative algorithm under the condition that the non-expanding operator T satisfies the semi-compactness or I-T satisfies the φ-extensibility.And they are applied to solving zero point problem and splitting feasible problem respectively.Secondly,in order to further optimize the generalized KM iterative algorithm,this paper proposes a generalized Ishikawa iterative algorithm with an error term.With the help of the previous research methods,this paper proves the strong and weak convergence theorems of the generalized Ishikawa iterative algorithm with error terms in Banach space,and illustrates the advantages of the generalized Ishikawa iterative algorithm with error term with examples.Finally,in order to further improve the variable generalized KM iterative algorithm,a variable generalized Ishikawa iterative algorithm is proposed.Using the previous research method,this paper proves the strong and weak convergence theorems of the variable generalized Ishikawa iterative algorithm in Banach space,and the conclusions obtained enrich the related theoretical achievements of KM iterative algorithm and Ishikawa iterative algorithm.