Variational Inclusions Involving (A,η)-Accretive Mappings In Banach Spaces

Variational inequality theory and complementary problem theory are very powerful tools of the current mathematical technology.Variational inclusions is an important and useful genrealization of variational inequality.Because of the wide applications in many fields,variational inequality and variational inlcusions have been studied by Noor,Huang,Chang,Ding,Kazmi,U-ko and other outhors at home and abroad.Variational inclusions is the theory of different operators and their solutions in different spaces.It mainly deals with the existence,uniqueness and related algorithms of the solution of variational inclusions.After more than a decade developing,the research range of this theory has extended from Hilbert spaces to Banach spaces.Especially,kinds of classical variational inclusions in Banach spaces have been introduced and studied by Chang,Cho, Lee and Jung,Zhang Shi-sheng,Huang Nan-jing,etc.The thesis is composed of four 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 artical.Secondly,we used the(H,η)-accretive mappings to discuss the convergence analysis of iterative algorthm for generalized nonlinear implicit quasi-variational inclusions in Banach spaces.Thirdly,by using the resolvent operator technique,we also construct a class of iterative algorthms for a class of relaxed cocoercive variational inclusions involving set-valued mappings,and study applications of (A,η)-accretive mappings to the approximation-solvability of the relaxed cocoercive variational inclusions in q-uniformly smooth Banach spaces.Finally,in q-uniformly smooth Banach spaces,we introduced a new conception of(A,f,η)-accretive mappings.By using the properties of(A,f,η)-accretive mappings and the generalized resovent operators technique,the solvability of a class of completely generalized implicit nonlinear variational inclusions is given.In all,the results presented in this paper extend and improved many known results in the literature.