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**Strong convergence of a hybrid iteration scheme for equilibrium problems, variational inequality problems and common fixed point problems, of quasi-\(\phi\)-asymptotically nonexpansive mappings in Banach spaces.**
*(English)*
Zbl 1325.47139

Summary: We introduce an iterative algorithm for finding a common element of the set of common fixed points of a finite family of closed quasi-\(\phi\)-asymptotically nonexpansive mappings, the set of solutions of an equilibrium problem, and the set of solutions of the variational inequality problem for a \(\gamma\)-inverse strongly monotone mapping in Banach spaces. Then we study the strong convergence of the algorithm. Our results improve and extend the corresponding results announced by many others.

### MSC:

47J25 | Iterative procedures involving nonlinear operators |

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

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\textit{J. Zhao}, J. Appl. Math. 2012, Article ID 516897, 19 p. (2012; Zbl 1325.47139)

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### References:

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