In 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 mono- tonicity. Some special cases are also considered. Our proof of convergence is very simple. Results proved in this paper may stimulate further research in this dynamic field.
Aslam Noor, M.; Inayat Noor, K.; and Al-Said, Eisa
"Iterative Methods for Solving Nonconvex Equilibrium Variational Inequalities,"
Applied Mathematics & Information Sciences: Vol. 06:
1, Article 8.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol06/iss1/8