Multivalued General Mixed Variational-like Inequalities And A New Class Of Variational Inclusions

Variational inequality theory and complementary problem theory are very powerful tools of the current mathematical technology. Variational inclusion is an important and useful generalization of variational inequality. Beacause of the wide applications in many fields, variational inequality and variational inclusion have been studied by Noor,Huang,Chang,Ding,Kazmi, U-ko and other authors at home and abroad.The main purpose of this thesis is to make discussion a new class of Variational Inclusions with Generalized m-Accretive Mappings and a new class of Multivalued General Mixed Variational-like Inequalities by using the resolvent operator technique and auxiliary principle technique.The thesis is composed of three sections. Firstly,we show the real background of the Variational inequality theory and the main works that have been studied by many authors, so as to show that our works worthy of attention.We also introduce some basic conceptions and our main results in this article. Secondly, we use the auxiliary principle technique to suggest a new class of predictor-corrector algorithims for solving multivalued General mixed Variational-like inequalities. We also prove that the convergence of the suggested methods In a weaker condition. finally,in Banach space, by using the resolvent operator technique we studied a class of variational inclusions with generalized m-accretive mapping and constructed some algorithms for approximating the solution of this class of variational inclusions with generalized m- accretive mapping.In all,the results presented in this paper extend and improve many known results in the literature.