Modified Relaxed Extragradient Method for a General System of Variational Inequalities and Nonexpansive Mappings in Banach Spaces

General Variational Inequalities and Nonexpansive Mappings in Hilbert Spaces

In this paper, we suggest and analyze a three-step iterative scheme for finding the common element of the set of the solutions of the general variational inequalities involving two nonlinear operators and the set of the common fixed point of nonexpansive mappings. We also consider the convergence analysis of the suggested iterative schemes under some mild conditions. Our results improve and ext...

The System of Vector Variational-like Inequalities with Weakly Relaxed ${eta_gamma-alpha_gamma}_{gamma inGamma}$ Pseudomonotone Mappings in Banach Spaces

In this paper, we introduce two concepts of weakly relaxed ${eta_gamma-alpha_gamma}_{gamma in Gamma}$ pseudomonotone and demipseudomonotone mappings in Banach spaces. Then we obtain some results of the solutions existence for a system of vector variational-like inequalities with weakly relaxed ${eta_gamma-alpha_gamma}_{gamma in Gamma}$ pseudomonotone and demipseudomonotone mappings in reflexive...

Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings

Based on the relaxed extragradient method and viscosity method, we introduce a new iterative method for finding a common element of solution of equilibrium problems, the solution set of a general system of variational inequalities, and the set of fixed points of a countable family of nonexpansive mappings in a real Hilbert space. Furthermore, we prove the strong convergence theorem of the studi...

Generalized Variational Inequalities Involving Relaxed Monotone Mappings and Nonexpansive Mappings

Modified Noor’s Extragradient Method for Solving Generalized Variational Inequalities in Banach Spaces

and Applied Analysis 3 2. Preliminaries Let C be a nonempty closed convex subset of a real Banach space E. Recall that a mapping A of C into E is said to be accretive if there exists j x − y ∈ J x − y such that 〈 Ax −Ay, j(x − y)〉 ≥ 0, 2.1 for all x, y ∈ C. A mapping A of C into E is said to be α-strongly accretive if, for α > 0, 〈 Ax −Ay, j(x − y)〉 ≥ α∥∥x − y∥∥2, 2.2 for all x, y ∈ C. A mappin...