Strong Convergence of Generalized Projection Algorithm for Variational Inequality Problems with Applications

Abstract

Let E be a 2-uniformly convex and uniformly smooth real Banach space with dual space E?. Let C be a nonempty closed and convex subset of E and let A : C ? E? be an ?-inverse strongly monotone map. Assume that the set of solutions of the variational inequality problem, V I(C, A), is nonempty. A generalized projection algorithm is constructed and proved to converge strongly to some x? ? V I(C, A). Our theorems are significant improvements on recent important results. Finally, applications of our theorems to convex minimization problems, zeros of ?-inverse strongly monotone maps and complementarity problems are presented.