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Zbl 0960.47036
Huang, Nan-Jing; Bai, Min-Ru; Cho, Yeol Je; Kang, Shin Min
Generalized nonlinear mixed quasi-variational inequalities.
(English)
[J] Comput. Math. Appl. 40, No.2-3, 205-215 (2000). ISSN 0898-1221

The problem is studied to find in a Hilbert space $u$, $x\in Su$, $y\in Tu$, and $z\in Gu$ such that the inclusion $0\in N(x,y)+M(p(u),z)$ holds. Here, $M(\cdot,z)$ is assumed to be maximal monotone where the resolvent $(I+\rho M(\cdot,z))^{-1}$ is Lipschitz with respect to $z$; $S,T,G$ are Lipschitz with respect to the Hausdorff distance, and for $p$ and $N$ Lipschitz and monotonicity conditions are assumed (always with appropriate constants). \par An iterative algorithm is suggested whose convergence to a solution is proved. Moreover, for single-valued $S,T$ and $G=I$ also stability of a perturbed algorithm is proved.
[Martin Väth (Würzburg)]
MSC 2000:
*47J20 Inequalities involving nonlinear operators
47J25 Methods for solving nonlinear operator equations (general)
47H05 Monotone operators (with respect to duality)
49J40 Variational methods including variational inequalities

Keywords: iterative algorithm; stability; nonlinear quasi-variational inclusion; mixed quasi-variational inequality; maximal monotone operator

Cited in: Zbl 1098.47063 Zbl 1060.65064

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