EQUILIBRIUM PROBLEMS AND VARIATIONAL INEQUALITIES
Muhammad Aslam Noor, Khalida Inayat Noor · 2005
In this paper, we suggest and analyze some iterative methods for solving equilibrium problems with trifunction by using the auxiliary principle technique. We prove that the convergence of the proposed methods either re- quires only pseudomonotonicity or partially relaxed strongly monotonicity. We also consider the concept of well-posedness for equilibrium problems with tri- function and obtain some new results. It is shown that the auxiliary principle technique developed in this paper can be extended for regularized equilibrium problems with some minor modifications. Since equilibrium problems with tri- function include the classical equilibrium problems, variational inequalities and complementarity problems as special cases, results proved in this paper continue to hold for these problems. Our results can be viewed as a novel application of the auxiliary principle technique. MSC 2000. 49J40, 90C33, 35A15.