Auxiliary principle technique for equilibrium problems. (English) Zbl 1092.49010
Summary: We use the auxiliary principle technique to suggest and analyze a number of iterative methods for solving mixed quasiequilibrium problems. We prove that the convergence of these new methods requires either partially relaxed strongly monotonicity or peudomonotonicity, which is a weaker condition than monotonicity. Our proof of convergence is very simple as compared with others. These new results include several new and known results as special cases. Our results represent refinement and improvement of the previous known results for equilibrium and variational inequalities problems.
MSC:
| 49J40 | Variational inequalities |
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
| 91B50 | General equilibrium theory |
Keywords:
equilibrium problems; variational inequalities; auxiliary principle; proximal methods; convergence; skew-symmetric functionsReferences:
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