Some Iterative Methods for Solving Nonconvex Bifunction Equilibrium Variational Inequalities

On nonconvex bifunction variational inequalities

In this paper, we introduce and consider a new class of variational inequalities, which is called the nonconvex bifunction variational inequality. We suggest and analyze some iterative methods for solving nonconvex bifunction variational inequalities using the auxiliary principle technique.We prove that the convergence of implicit method requires only pseudomonotonicity, which is weaker conditi...

Iterative Methods for Solving Nonconvex Equilibrium Variational Inequalities

n this paper, we introduce and consider a new class of equilibrium problems and variational inequalities which is called the nonconvex equilibrium variational inequality. We suggest and analyze some iterative methods for solving the nonconvex equilibrium variational inequalities using the auxiliary principle technique. We prove that the convergence of implicit method requires only monotonicity....

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Convergence Theorems of Iterative Methods for System of Nonconvex Variational Inequalities

In this paper, we suggest and analyze some iterative methods for solving the system of nonconvex variational inequalities with two nonlinear mappings by using the projection technique. We show that the strong convergence of these iterative methods to the solutions of the system of nonconvex variational inequalities. Consequently, the results presented in this paper can be viewed as an improveme...

Some Extragradient Methods for Nonconvex Quasi Variational Inequalities (communicated by M.s.moslehian)

In this paper, we introduce and consider a new class of variational inequalities involving two operators, which is called the general nonconvex quasi variational inequality. Several special cases are discussed. We use the projection technique to establish the equivalence between the general nonconvex quasi variational inequalities and the fixed point problems. This alternative equivalent formul...