A Hybrid Extragradient Method for Solving Ky Fan Inequalities, Variational Inequalities and Fixed Point Problems
Supak Phiangsungnoen, Poom Kumam · 2013
The purpose of this paper is to introduce a new hybrid extragradient iterative method for finding a common element of the set of points satisfying the Ky Fan inequalities, variational inequality and the set of fixed points of a strict pseudocontraction mapping in Hilbert spaces. Consequently, we obtain the strong convergence of an iterative algorithm generated by the hybrid extragradient projection method, under some suitable assumptions the function associated with Ky Fan inequality is pseudomonotone and weakly continuous. Index Terms—Extragradient Method, Fixed point problems, Hybrid projection method,Variational inequality problems, strict pseudocontraction, Lipschitz continuity.