A Hybrid Extragradient Viscosity Approximation Method for Solving Equilibrium Problems and Fixed Point Problems of Infinitely Many Nonexpansive Mappings

作者：Jaiboon Chaichana; Kumam Poom^*

来源：Fixed Point Theory and Applications, 2009, 2009(1): 374815.

DOI：10.1155/2009/374815

We introduce a new hybrid extragradient viscosity approximation method for finding the common element of the set of equilibrium problems, the set of solutions of fixed points of an infinitely many nonexpansive mappings, and the set of solutions of the variational inequality problems for beta-inverse-strongly monotone mapping in Hilbert spaces. Then, we prove the strong convergence of the proposed iterative scheme to the unique solution of variational inequality, which is the optimality condition for a minimization problem. Results obtained in this paper improve the previously known results in this area.

• 出版日期2009