In this paper, we consider and analyze a new extragradient method for solving pseudomonotone variational inequalities. The new method converges for pseudomonotone Lipschitz continuous operators, which is a weaker condition than monotonicity. The new iterative method includes the extragradient method as a special case. Our proof of convergence is very simple as compared with other methods. Mathe...

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 projec...

In this paper, we introduce and analyze a hybrid steepest-descent extragradient algorithm for solving triple hierarchical pseudomonotone variational inequalities in a real Hilbert space. The proposed algorithm is based on Korpelevich’s extragradient method, Mann’s iteration method, hybrid steepest-descent method and Halpern’s iteration method. Under mild conditions, the strong convergence of th...

In this paper, we propose a new version of extragradient method for the variational inequality problem. The method uses a new searching direction which differs from any one in existing projection-type methods, and is of a better stepsize rule. Under a certain generalized monotonicity condition, it is proved to be globally convergent. @ 2001 Eisevier Science Ltd. All rights reserved. Keywords-Vs...

We propose a modification of the classical extragradient and proximal point algorithms for finding a zero of a maximal monotone operator in a Hilbert space. At each iteration of the method, an approximate extragradient-type step is performed using information obtained from an approximate solution of a proximal point subproblem. The algorithm is of a hybrid type, as it combines steps of the extr...

‎In this paper‎, ‎we propose two iterative methods for finding a common solution of a finite family of equilibrium problems ‎for pseudomonotone bifunctions‎. ‎The first is a parallel hybrid extragradient-cutting algorithm which is extended from the‎ ‎previously known one for variational inequalities to equilibrium problems‎. ‎The second is a new cyclic hybrid‎ ‎extragradient-cutting algorithm‎....