The Research On Convergence Of Solution Of The Quasi Variational Inclusion Problems With Applications

The quasi-variational inclusion problem,which was proposed based on the variational inclusion problem and variational inequality problem,is an important class of nonlinear problems.As we all know,the accurate solution of the quasi-variational inclusion problem is usually diffcultly to obtain.Therefore,domestric and oversea scholars always use the iterative algorithms to generate a conver-gence sequence to obtain its approximate solution.At present,many iterative algorithms have been proposed to solve quasi variational inclusion problem,and many conclusions have been obtained.However,in practice,the convergence rate of the algorithm affects the processing result of the problem to some extent,so it is a meaningful work to improve and optimize of the algorithmIn virtue of thoughts and research experience of scholars,we first investigate the convergence of solution of the quasi-variational inclusion problem in Hilbert space.Secondly,we investigate the convergence of soultion of the quasi-variational inclusion problem in uniformly convex and 2-uniformly smooth Banach space.Th-irdly,we investigate the convergence of the solution of the system of quasi-variational inclusion problems in uniformly convex and q-uniformly smooth Banach space.Finally,some research results in this field are used to solve other problems.We discuss the following three aspects in this thesisFirstly,the research about background,significiance and actualities of the quasi-variational inclusion problem are briefly introduced,and the research con-tent of quasi-variational inclusion problem and the innovation of the thesis are further clarified.Secondly,based on the means of the idea of forward-backward splitting method and shrinking projection method,a new iterative algorithm is construct-ed.A convergence of the solution of the quasi-variational inclusion problem in Hilbert space is studied,and the strong convergence of solution for quasi-variational inclusion problem is obtained.Thirdly,based on the ideas of the forward-backward splitting method and the shrinking projection method,an iterative algorithm is constructed.The con-vergence of solution of the quasi-variational inclusion problem in uniformly convex and 2-uniformly smooth Banach space is studied.Finally,the strong convergence of the solutions of the quasi variational inclusion problems is obtained.Fourthly,based on the existing idea of the forward-backward splitting method,the strong convergence of common solution of the system of quasi-variational in-clusion problem in uniformly convex and q-uniformly smooth Banach space is obtained.