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**Weak convergence theorems for strictly pseudocontractive mappings and generalized mixed equilibrium problems.**
*(English)*
Zbl 1381.47050

Summary: We introduce a new iterative method for finding a common element of the set of fixed points of a strictly pseudocontractive mapping, the set of solutions of a generalized mixed equilibrium problem, and the set of solutions of a variational inequality problem for an inverse-strongly-monotone mapping in Hilbert spaces and then show that the sequence generated by the proposed iterative scheme converges weakly to a common element of the above three sets under suitable control conditions. The results in this paper substantially improve, develop, and complement the previous well-known results in this area.

### MSC:

47J25 | Iterative procedures involving nonlinear operators |

47H05 | Monotone operators and generalizations |

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

### Keywords:

iterative method; strictly pseudocontractive mapping; inverse-strongly-monotone mapping; Hilbert spaces
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\textit{J. S. Jung}, J. Appl. Math. 2012, Article ID 384108, 18 p. (2012; Zbl 1381.47050)

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### References:

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