*Correspondence: [email protected] 1School of Information Engineering, North China University of Water Resources and Electric Power, Zhengzhou, Henan 450011, China Full list of author information is available at the end of the article Abstract In this article, variational inequality, fixed point, and generalized mixed equilibrium problems are investigated based on an extragradient iterative algor...

The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a monotone, Lipschitz continuous mapping. We introduce an extragradient-like approximation method which is based on so-called extragradient method and viscosity approximation method. We establish...

In this paper we analyze the iteration-complexity of the hybrid proximal extragradient (HPE) method for finding a zero of a maximal monotone operator recently proposed by Solodov and Svaiter. One of the key points of our analysis is the use of a new termination criteria based on the εenlargement of a maximal monotone operator. The advantages of using this termination criterion it that its defin...

Recently, Nemirovski’s analysis indicates that the extragradient method has the O(1/t) convergence rate for variational inequalities with Lipschitz continuous monotone operators. For the same problems, in the last decades, we have developed a class of Fejér monotone projection and contraction methods. Until now, only convergence results are available to these projection and contraction methods,...

Abstract In this paper, we introduce a Totally Relaxed Self-adaptive Subgradient Extragradient Method (TRSSEM) with Halpern iterative scheme for finding common solution of Variational Inequality Problem (VIP) and the fixed point quasi-nonexpansive mapping in 2-uniformly convex uniformly smooth Banach space. The TRSSEM does not require computation projection onto feasible set VIP; instead, it us...

In this paper, we introduce the extragradient method for finding a common element of the set of solutions of generalized mixed equilibrium problem, the set of common fixed point of family of nonexpansive mappings the set of variational inequality for monotone, Lipschitz continuous mapping in a Hilbert space. Then we prove the strong convergence of iterative algorithm to a common element of this...

‎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....

We propose a hybrid extragradient method for finding a common element of the solution set of a variational inequality problem, the solution set of a general system of variational inequalities, and the fixed-point set of a strictly pseudocontractive mapping in a real Hilbert space. Our hybrid method is based on the well-known extragradient method, viscosity approximation method, and Mann-type it...

We investigate the problem of finding a common solution of a general system of variational inequalities, a variational inclusion, and a fixed-point problem of a strictly pseudocontractive mapping in a real Hilbert space. Motivated by Nadezhkina and Takahashi’s hybrid-extragradient method, we propose and analyze new hybrid-extragradient iterative algorithm for finding a common solution. It is pr...