In the present paper, we introduce the concept of η-cocoercivity of a map and develop some iterative schemes for finding the approximate solutions of mixed variational-like inequalities. We use the concept of η-cocoercivity to prove the convergence of the approximate solutions to the exact solution of mixed variational-like inequalities.

The local boundedness of weak solutions to variational inequalities (obstacle problem) with the linear growth condition is obtained. Consequently, an analogue of a theorem by Reshetnyak about a.e. differentiability of weak solutions to elliptic divergence type differential equations is proved for variational inequalities.

A generalized proximal point method for solving variational inequalities with maximal monotone operators is developed. It admits a successive approximation of the feasible set and of a symmetric component of the operator as well as an inexact solving of the regularized problems. The conditions on the approximation are coordinated with the properties of finite element methods for solving problem...

‎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 study a class of second order nonlinear variational inequalities with bilateral constraints. This type of inequalities arises in zero sum stochastic differential games of mixed type where each player uses both continuous control and stopping times. Under a nondegeneracy assumption Bensoussan and Friedman [1,4] have studied this type of problems. They proved the existence of a unique solution...

Variational inequalities are being used as a mathematical programming tool in modeling a wide class of problems arising in different branches of pure and applied sciences, see [1–26]. Variational inequalities have been extended and generalized in various directions using novel and innovative techniques. A useful and important generalization is called the general variational inclusion involving ...