Generalized Projection Algorithm to Approximating the Solutions of One Kind of Variational Inequalities

Finding suitable algorithms to approximate the solution of variational inequalities is a very active topic in different branches of mathematical fields since it plays a significant role in economics, finance, transportation, elasticity, optimization, operations research and structural analysis, etc. Considerable research efforts have been devoted to the study of iterative schemes of approximating the solution of variational inequalities in recent years. By now, there already exist some algorithms, but they are not quite enough to deal with problems related to more general operators defined in a more general space. In this paper, a new generalized projection algorithm is introduced which is proved to be strongly convergent to the solution of one kind of variational inequalities in Banach space by using some techniques of Lyapunov functional and generalized projection operator, etc.