A new hybrid algorithm for variational inclusions, generalized equilibrium problems, and a finite family of quasi-nonexpansive mappings.

*(English)*Zbl 1186.47060Summary: We propose a new iterative scheme for finding common elements of the set of fixed points of a finite family of quasi-nonexpansive mappings, the set of solutions of variational inclusions, and the set of solutions of generalized equilibrium problems. Some strong convergence results are derived by using the concept of \(W\)-mappings for a finite family of quasi-nonexpansive mappings under suitable conditions in Hilbert spaces.

##### MSC:

47J25 | Iterative procedures involving nonlinear operators |

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

47J22 | Variational and other types of inclusions |

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