Variational Inclusions In Banach Spaces

It is known that, we solve the problems of variational inequalities always using Projection methods and Wiencr-Hopf equation methods. However, it's not efficient to mixed variational inequalities. Therefore, the authors will creat and use resolvent operators to solve problems. On the basis of Huang and Fang's work, we continue to study the variational inclusions in this paper.In the introduction, we mainly introduce the origin, development and application of variational inequalities.In chapter one, we mainly introduce the definitions and properties of accretive operators. In the terms of the new resolvent operator technique, we give the approximate solution for a class of variational inclusions involving H-accretive operators in Banach spaces.In chapter two, we mainly introduce the definitions and properties of monotone operators. Using the resolvent operator associated with (H, η)-monotone operators, we prove the existence and uniqueness of solutions for the new system of variational inclusions. We also construct the iterative algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates.