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**A new general iterative method for solution of a new general system of variational inclusions for nonexpansive semigroups in Banach spaces.**
*(English)*
Zbl 1221.47110

Summary: We introduce a new general system of variational inclusions in Banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mapping and the set of fixed points of nonexpansive semigroups in a uniformly convex and 2-uniformly smooth Banach space. Furthermore, strong convergence theorems are established under certain control conditions. As applications, finding a common solution for a system of variational inequality problems and minimization problems is treated.

### MSC:

47J22 | Variational and other types of inclusions |

47J25 | Iterative procedures involving nonlinear operators |

47H20 | Semigroups of nonlinear operators |

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

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\textit{P. Sunthrayuth} and \textit{P. Kumam}, J. Appl. Math. 2011, Article ID 187052, 29 p. (2011; Zbl 1221.47110)

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### References:

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