The Research On Strong Convergence Of Solutions Of The Split Variational Inequality Problems

The split variational inequality problem,which was proposed by basing on the variational inequality problem and split feasibility problem,is an important class of nonlinear problems.As we all know,it is difficult to find the accurate solutions of the split variational inequality problem.Therefore,domestic and overseas scholars always use the iterative algorithm to generate a convergence sequence to obtain its approximate solutions.Most of the existing algorithms can only get weak convergence of solutions.Hence,in this thesis,by improving the iterative algorithms,new iterative algorithms with strong convergence are introduced to solve this problem in Hilbert space and Banach space,respectively First of all,based on the idea of Halpern iteration,a new iterative algorithm was proposed to approximate a solution of the split variational inequality problem in Hilbert spaces,and a strong convergence theorem was obtained,meanwhile,the iterative algorithm was utilized to solve other nonlinear problems.Secondly,based on the idea of the viscosity algorithm,an iterative algorithm was constructed with the help of sunny nonexpansive retract mapping to solve the split generalized variational inequality problem in Banach spaces,and the main results presented in this thesis were used to solve the equilibrium problem and zero point problem.