The system of nonlinear variational inequalities (SNVI) is a useful generalization of variational inequalities. Verma (2001) suggested and analyzed an iterative method for solving SNVI. In this paper, we present a new self-adaptive method, whose computation cost is less than that of Verma’s method. The convergence of the new method is proved under the same assumptions as Verma’s method. Some pr...

The Schwarz algorithm for a class of elliptic quasi-variational inequalities with nonlinear source terms is studied in this work. The authors prove a new error estimate in uniform norm, making use of a stability property of the discrete solution. The domain is split into two sub-domains with overlapping non-matching grids. This approach combines the geometrical convergence of solutions and the ...

Recently, Fukushima proposed a diierentiable optimization framework for solving strictly monotone and continuously diierentiable variational inequalities. The main result of this paper is to show that Fukushima's results can be extended to monotone (not necessarily strictly monotone) and Lipschitz continuous (not necessarily continuously diierentiable) variational inequalities, if one is willin...

In this paper, we consider and analyze a new class of extragradient-type methods for solving general variational inequalities. The modified methods converge for pseudomonotone operators which is weaker condition than monotonicity. Our proof of convergence is very simple as compared with other methods. The proposed methods include several new and known methods as special cases. Our results prese...

We study in this paper the existence and approximation of solutions of variational inequalities involving generalized pseudo-contractive mappings in Banach spaces. The convergence analysis of a proposed hybrid iterative method for approximating common zeros or fixed points of a possibly infinitely countable or uncountable family of such operators will be conducted within the conceptual framewor...

We consider a class of monotone variational inequalities in which both the operator and the convex set are parametrized by continuous functions. Under suitable assumptions, we prove the continuity of the solution with respect to the parameter. As an important application, we consider the case of finite dimensional variational inequalities on suitable polyhedra. We demonstrate the applicability ...

In this paper, we introduce two iterative algorithms (one implicit algorithm and one explicit algorithm) for finding a common element of the solution set of a general system of variational inequalities for continuous monotone mappings and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. First, this system of variational inequalities is proven to be equivalent to...

The aim of this paper is to study the continuity of the solutions to degenerate time-dependent variational inequalities. In order to obtain the continuity of the solution, a previous continuity result (see [1]) for strongly monotone variational inequalities and an appropriate use of the convergence set in Mosco’s sense play an important role. The continuity result allows us to provide a discret...

In this paper, we introduce an iterative sequence by using a hybrid generalized f−projection algorithm for finding a common element of the set of fixed points of a relatively weak nonexpansive mapping and the set of solutions of a generalized variational inequality in a Banach space. Our results extend and improve the recent ones announced by Y. Liu [Strong convergence theorems for variational ...

CCC 0749-159X/93/010023-11 Numerical Methods for Partial Differential Equations, 9, 23-33 (1993) \!:) 1993 John Wiley & Sons, Inc. Local a posteriori error estimators for finite element approximation o( variational inequalities are derived. These are shown to provide upper bounds on the discretization error. Numerical examples are given illustrating the theoretical results. © 1993 John Wiley an...