Iterative Algorithm For A System Of Nonlinear Implicit Variational Inequalities And Variational Inclusions

Variational Inequalities problems are an important branch of the con-trol theory and optimization,it have played a wide range of application in several fields such as physics,engineering mechanics,mathematical finance and others.The paper mainly studies iterative algorithm for a system of nonlinear implicit variational inequalities and variational inclusionssome,and under weak conditions proves the convergence of iterative algorithm.The first chapter is the brief introduction of variational inequality; The second chapter mainly studies the approximation-solvability of nonlinear implicit varia-tional inequalities,First,the general iterative algorithm for nonlinear implicit varia-tional inequalities is introduced;Second,we improve that the iterative sequences gen-erated by the Iterative algorithm converges to the solver of nonlinear implicit vari-ational inequalities.The third chapter mainly studies the approximation-solvability of nonlinear implicit variational inequalities,First,two-step projection methods for nonlinear implicit Variational Inequalities is introduced;Second,the iterative se-quences generated by the two-step projection methods is improved to converge to the solver of nonlinear implicit Variational Inequalities;The fourth chapter studies the approximation-solvability of variational inclusions,First, we introduced a new class of A-monotone mapping of variational inclusions problems, through the A- monotone mapping proximity mapping, this paper gives a class of Variational In-clusions Problems,second we construct a new iterative algorithm for solving this system of variational inclusions in real smooth Banach spaces.The results obtained in this paper extend and improved the recently results.