In this paper, we combine the subgradient extragradient method with the Halpern method for finding a solution of a variational inequality involving a monotone Lipschitz mapping in Banach spaces. By using the generalized projection operator and the Lyapunov functional introduced by Alber, we prove a strong convergence theorem. We also consider the problem of finding a common element of the set o...

Let C be a nonempty closed convex subset of a real Hilbert space H. Let S : C → C be an asymptotically nonexpansive map in the intermediate sense with the fixed point set F (S). Let A : C → H be a Lipschitz continuous map, and V I(C,A) be the set of solutions u ∈ C of the variational inequality 〈Au, v − u〉 ≥ 0, ∀v ∈ C. The purpose of this work is to introduce a hybrid extragradient-like approxi...

Correspondence: jwpeng6@yahoo. com.cn School of Mathematics, Chongqing Normal University, Chongqing 400047, PR China Abstract In this article, we introduce some new iterative schemes based on the extragradient method (and the hybrid method) for finding a common element of the set of solutions of a generalized equilibrium problem, and the set of fixed points of a family of infinitely nonexpansiv...

In this paper, we consider the algorithm proposed in recent years by Censor, Gibali and Reich, which solves split variational inequality problem, and Korpelevich's extragradient method, which solves variational inequality problems. As our main result, we propose an iterative method for finding an element to solve a class of split variational inequality problems under weaker conditions and get a...

In this paper, we introduce inertial Tseng’s extragradient algorithms combined with normal-S iteration process for solving variational inequality problems involving pseudo-monotone and Lipschitz continuous operators. Under mild conditions, establish the weak convergence results in Hilbert spaces. Numerical examples are also presented to show that faster behaviour of proposed method.

The purpose of this paper is to consider a new scheme by the hybrid extragradient-like method for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a variational inequality, and the set of fixed points of an infinitely family of strictly pseudocontractive mappings in Hilbert spaces. Then, we obtain a strong convergence theorem o...