A hybrid extragradient viscosity approximation method for solving equilibrium problems and fixed point problems of infinitely many nonexpansive mappings.

*(English)*Zbl 1186.47065From the summary: 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 infinitely many nonexpansive mappings, and the set of solutions of the variational inequality problem for a \(\beta \)-inverse-strongly monotone mapping in Hilbert spaces. Then, we prove the strong convergence of the proposed iterative scheme to the unique solution of a variational inequality, which is the optimality condition for a minimization problem.

##### MSC:

47J25 | Iterative procedures involving nonlinear operators |

47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |

##### Keywords:

viscosity approximation method; equilibrium problems; fixed points; variational inequality problems; strong convergence
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\textit{C. Jaiboon} and \textit{P. Kumam}, Fixed Point Theory Appl. 2009, Article ID 374815, 32 p. (2009; Zbl 1186.47065)

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