Generalized F-projection For Generalized Variational Inequality

In this paper, we present a modification of a double projectionalgorithm proposed by Solodov and an extragradient method proposed by Wangto find a solution of a class of generalized variational inequalities in Hilbert space.The main modification of the two methods is to chang metric projection into gen-eralized f-projection, for solving the generalized variational inequality. Globalconvergence of the two methods is guaranteed when F is psudomonotone contin-uous mapping and f is a proper, convex, and lower semi-continuous functionalin Hilbert space. Finally we add a perturbation in generalized f-projection algo-rithm and the perturbed method is also proved to be globally convergent undervery mild assumption.