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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.
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