Iterative Algorithm For A Class Of Variational Inequality In Hilbert Space

The variational inequality play a irreplaceable role in the mathematics.It iswidely used in control theory, operator theory, optimization theory, economic decision-making. In the paper, using the fixed point theory studied the iterative algorithmof the solutions of a class of variational inequalities in Hibert space.The iterationscheme is given by three methods.The second chapter, using the equivalence relationof variational inequality and Wiener-Hopf equation, constructs the first iterationscheme for synchronization solution the iterative scheme of nonexpansive mappingfixed point and variational inequality, and under certain conditions, the convergencecondition of strict proof is given. In the third chapter, second iterative scheme isgiven by using the projection method and solve the variational inequality whichcontent of k-strictly pseudocontractive, some conclusions of predecessors are ex-tended. The fourth chapter, the third iterative scheme is given by the algorithm ofviscosity method. And the convergence is strictly proved. the previous conclusionsare generalized to k-strictly pseudocontractive.