Random Vector F-implicit Complementary Problems And Generalized Variational Inclusion's Problems

Variational inequality theory has been prominent in mathematics.Among many aspects of it,the most important and interesting is to develop effective numerical methods to generate approximate solutions.This paper will discuss it in the following way:Firstly,the background and current state of variational inequality theorywill be discussed.Secondly,it will introduces and studies a new class of random vector problemsFimplicit complementary problems and random vector F-implicit variational inequality problems,and the equivalence of them is presented under certain assumption in Banach space.Some new existence theorems of solutions for the random vector F-implicit complementary problems and random vector F-implicit variational inequality problems are derived under some suitable conditions.Thirdly,it will introduces and studies a system of generalized variational-like inclusions with(A,η)-accretive operators in q-uniformly smooth Banach space.By applying the resolvent operators,the iterative algorithm for solving this system of generalized variational-like inclusions in q-uniformly smooth Banach space is established. And it will proves the existence of solution for the generalized variational-like inclusions and the convergence of iterative sequences generated by algorithm.Finally,it will introduces the concept of the(A,η,g)-accretive operators and study a system of generalized variational-like inclusions with(A,η,g)-accretive operators in q-uniformly smooth Banach space.By applying the resolvent operators associated with(A,η,g)-accretive operators,a new p-step iterative algorithm for solving this system of generalized variational-like inclusions in q-uniformly smooth Banach space is established.And it will proves the existence of solution for the generalized variational-like inclusions and the convergence of iterative sequences generated by algorithm.