Iterative Appraximation Of Solutions And Their Applications For Several Generalized Split Feasibility Problems

This thesis mainly investigate several generalized split feasibility problems.We propose several algorithms for solving these problems and establish their weak or strong convergence theorems under certain conditions.The results presented in this paper extend and improve some corresponding results in the literature.This thesis consists of six chapters.In Chapter 1,we introduce the research background and present situation of several generalized split feasibility problems,and also state the main work of this thesis.In Chapter 2,we recall some basic concepts and theories.In Chapter 3,we study the split monotone variational inclusion,variational inequality and a fixed point problem of a finite family of strict psedo-contractions.We construct an appropriate iterative algorithm to approximate the common solution of the problems above by using projection method.Under some suitable conditions,we prove a strong convergence theorem for the iterative algorithm.Numerical example illustrates the feasibility of theoretical result.In Chapter 4,we study split equilibrium problems,variational inequalities problem and fixed point problem of an asymptotically nonexpansive semigroup.We construct an appropriate iterative algorithm to approximate the common solution of the problems above by using demiclosedness principle of nonexpansive mapping and asymptotically nonexpansive mapping.Under some suitable conditions,we prove a strong convergence theorem for the iterative algorithm.Numerical examples illustrate the feasibility of theoretical result.In Chapter 5,we study a split common fixed point problem involved in a finite family of nonexpansive mappings and strictly pseudo-nonspreading mappings and a split combination of a finite family of variational inequalities problem.We construct an appropriate iterative algorithm to approximate the common solution of the problems above by using viscosity technique,demiclosedness principle of strictly pseudo-nonspreading mappings and Opial's condition.Under some suitable conditions,we prove a strong convergence theorem for the iterative algorithm.Numerical examples illustrate the feasibility of theoretical result.In Chapter 6,we study multiple-sets split feasibility problem and the split equality fixed point problem involved in firmly quasi-nonexpansive mappings.We construct an appropriate iterative algorithm to approximate the common solution of the problems above by using projection method and the properties of firmly quasi-nonexpansive mappings.Under very mild conditions,we prove a weak convergence theorem for our algorithm.Numerical examples illustrate the feasibility of theoretical result.