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| Volume 9, Number 2, August 2008, pp. 283-294 | |||||||
| Paul-Emile Maingé and Abdellatif Moudafi | |||||||
| Key words: | |||||||
| Fixed point problem, variational inequality, monotone mapping; equilibrium problem, hybrid steepest descent, extragradient methodooperative games, random order values, hedonic games, top coalition property | |||||||
| Mathematices Subject Classification: Primary 90C25, 49M45, 65C25. | |||||||
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| Abstract: | |||
| We make use of the viscosity technique to develop a convergent method for approximating a common element of the set of fixed points of a demicontractive operator and the set of solutions of a monotone equilibrium problem. The proposed algorithm is obtained by coupling a modified hybrid steepest descent method with the extragradient algorithm. Under mild conditions, the strong convergence of the sequences generated by the algorithm is obtained. Using this result we obtain two corollaries which improve or develop several corresponding results in this field. | |||
| Coupling viscosity methods with the extragradient algorithm for solving equilibrium problems | ||