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Auxiliary principle technique for solving generalized set-valued nonlinear quasi-variational-like inequalities. (English) Zbl 1031.49015

Summary: We introduce and study a new class of generalized set-valued nonlinear quasi-variational-like inequalities in Hilbert spaces and construct some iterative algorithms to compute the approximating solutions of this class inequalities by using the auxiliary principle technique. We also give the convergence analysis of the iterative sequences generated by the algorithms. The results presented in this paper extend and improve the corresponding results announced by Ding.

MSC:

49J40 Variational inequalities
47H10 Fixed-point theorems
49J53 Set-valued and variational analysis
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