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A new system of set-valued variational inclusions with \(H\)-monotone operators. (English) Zbl 1070.49007

Summary: The purpose of this paper is to introduce and study a new system of set-valued variational inclusions with \(H\)-monotone operators in Hilbert spaces. By using the resolvent operator method associated with \(H\)-monotone operators due to Y. Fang and N. Huang [Appl. Math. Comput. 145, No. 2–3, 795–803 (2003; Zbl 1030.49008)], we construct a new iterative algorithm for solving this kind of system of set-valued variational inclusions. We also prove the existence of solutions for this system and the convergence of iterative sequences generated by the algorithm.

MSC:

49J40 Variational inequalities
47H10 Fixed-point theorems

Citations:

Zbl 1030.49008
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