Fixed Point Iteration Methods For Several Classes Of Nonlinear Operators And Split Feasibility Problems

In this paper,we propose some iterative algorithms for solving the split feasible problems?the fixed point problems and the variational inequality problems for some classes of nonlinear operators in real Hilbert spaces,and prove weak convergence theorems for pseudo-contractive mappings,non-expansive mappings and monotone mappings.This paper is divided into the following four parts.The first chapter recalls the research of split feasible problems and fixed point problems,and describes the work of this paper.In the second chapter,we give some concepts and some preliminary results.In Chapter3,new algorithms is proposed,which embed the Ishikawa type iterative algorithms and the extra-gradient iterative algorithms to find a common solution of the splitting feasible problems and the fixed point problems of the L-Lipschitz continuous pseudo-contractive mappings;we also propose iterative algorithms for finding a common solution of the splitting feasible problems and the fixed point problems of the non-Lipschitz hypothesis pseudo-contractive mappings,that is,new algorithms of mutual embedding of Mann type iterative algorithms and extra-gradient iterative algorithms.It also studies a solution of the variational inequality constrained by the split feasible problem and the fixed point problem.The fourth chapter gives the remarks and prospect of this paper.In this paper,it is shown that the sequences generated by iterative algorithms are weakly convergent to a common solution of the splitting feasible problems and the fixed point problems under appropriate conditions.The results presented in this paper improve?extend and develop some recent corresponding ones in the literature.