Equilibrium Problems and Variational Inequalities
نویسندگان
چکیده
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 requires only pseudomonotonicity or partially relaxed strongly monotonicity. We also consider the concept of well-posedness for equilibrium problems with trifunction 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 trifunction 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.
منابع مشابه
Iterative algorithms for families of variational inequalities fixed points and equilibrium problems
متن کامل
A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems
متن کامل
Strong convergence for variational inequalities and equilibrium problems and representations
We introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for ...
متن کاملSome existence results for generalized vector quasi-equilibrium problems
In this paper, we introduce and study a class of generalized vector quasi-equilibrium problem, which includes many vector equilibrium problems, equilibrium problems, vector variational inequalities and variational inequalities as special cases. Using one person game theorems, the concept of escaping sequences and without convexity assumptions, we prove some existence results for ...
متن کاملAn Iterative Scheme for Generalized Equilibrium, Variational Inequality and Fixed Point Problems Based on the Extragradient Method
The problem ofgeneralized equilibrium problem is very general in the different subjects .Optimization problems, variational inequalities, Nash equilibrium problem and minimax problems are as special cases of generalized equilibrium problem. The purpose of this paper is to investigate the problem of approximating a common element of the set of generalized equilibrium problem, variational inequal...
متن کامل