The Split Variational Inequality, Split Mixed Equilibrium Problems And Their Convergence Algorithms

In this thesis, we will discuss two split variational inequality problems and the split mixed equilibrium problem, which generalize the split feasibility problem, the split common fixed point problem, the split variational inequality problems and the split equilibrium problem. This thesis was divided into five chapters.Chapter 1 is the introduction. We describe the develoption and the research situation of the split inverse problem.The second chapter is the preliminaries. The required definitions, positions and lemmas are presented.We propose a simple split variational inequality problem in the third chapter. We construct two iterative algorithms to solve the problem and obtain some strong and weak convergence theorems. The key of the study is to transform the split variational inequality problem into the fixed point problem.In Chapter 4, we study anther split variational inequality problem, which is the extension of the split variational inequality problem of the previous chapter. We also solve the problem by the Man and Helpen iterative algorithm.In the fifth chapter, we introduce a split mixed equilibrium problem. The split mixed equilibrium problem is transformed into the fixed point problem. Using the firmly nonexpansive position of the algorithm, we construct three iterative algorithms to solve this problem in real Hilbert space.