and Applied Analysis 3 which is called the general variational inequality, introduced and studied by Noor 19 . It has been shown that the minimum of a class of differentiable functions can be characterized by the general variational inequality of type 2.3 . B If g ≡ I, the identity operator, then 2.1 reduces to find u ∈ C and w ∈ A u such that 〈F u w,v − u〉 ≥ 0, ∀v ∈ C, 2.4 which is known as th...

In this paper, we introduce a new iterative sequence which is constructed by using the hybrid projection method for solving the common solution for a system of generalized equilibrium problems of inverse strongly monotone mappings and a system of bifunctions satisfying certain the conditions, the common solution for the families of quasi -φasymptotically nonexpansive and uniformly Lipschitz con...

The variational inequality problem is reduced to an optimization problem with a di erentiable objective function and simple bounds. Theoretical results are proved, that relate stationary points of the minimization problem to solutions of the variational inequality problem. Perturbations of the original problem are studied and an algorithm that uses the smooth minimization approach for solving m...

We establish the existence and uniqueness results for variational inequality problems on Riemannian manifolds and solve completely the open problem proposed in [21]. Also the relationships between the constrained optimization problem and the variational inequality problems as well as the projections on Riemannian manifolds are studied. Keyword: Variational inequalities; Riemannian manifold; Mon...

We introduce a new method for a system of generalized equilibrium problems, system of variational inequality problems, and fixed point problems by using S-mapping generated by a finite family of nonexpansive mappings and real numbers. Then, we prove a strong convergence theorem of the proposed iteration under some control condition. By using our main result, we obtain strong convergence theorem...

Variational inequalities have found many applications in applied science. A partial list includes obstacles problems, fluid flow in porous media, management science, traffic network, and financial equilibrium problems. However, solving variational inequalities remain a challenging task as they are often subject to some set of complex constraints, for example the obstacle problem. Domain decompo...

In this paper, we discuss smoothing approximations of nonsmooth functions arising from complementarity and variational inequality problems. We present some new results which are essential in designing Newton-type methods. We introduce several new classes of smoothing functions for nonlinear complementarity problems and order complementarity problems. In particular, in the first time some comput...