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**System of nonlinear set-valued variational inclusions involving a finite family of \(H(\cdot, \cdot)\)-accretive operators in Banach spaces.**
*(English)*
Zbl 1252.49024

Summary: We study a new system of nonlinear set-valued variational inclusions involving a finite family of \(H(\cdot, \cdot)\)-accretive operators in Banach spaces. By using the resolvent operator technique associated with a finite family of \(H(\cdot, \cdot)\)-accretive operators, we prove the existence of the solution for the system of nonlinear set-valued variational inclusions. Moreover, we introduce a new iterative scheme and prove a strong convergence theorem for finding solutions for this system.

### MSC:

49J53 | Set-valued and variational analysis |

47H06 | Nonlinear accretive operators, dissipative operators, etc. |

### Keywords:

nonlinear set-valued variational inclusions; finite family of \(H(\cdot, \cdot)\)-accretive operators; resolvent operator technique
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\textit{P. Junlouchai} and \textit{S. Plubtieng}, J. Appl. Math. 2012, Article ID 560248, 15 p. (2012; Zbl 1252.49024)

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### References:

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