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Perturbed Ishikawa type iterative algorithm for generalized quasivariational inclusions. (English) Zbl 1030.65071

The author considers a class of generalized nonlinear implicit quasivariational inclusions in a Hilbert space, which contains many classes of variational inclusions and variational inequalities. This problem is converted into a fixed point problem, so that the problem can be solved with the help of modified Ishikawa and Mann algorithms. Their convergence is established under additional Lipschitz continuity and strong monotonicity assumptions.
Reviewer: I.V.Konnov (Kazan)

MSC:

65K10 Numerical optimization and variational techniques
49J40 Variational inequalities
49M25 Discrete approximations in optimal control
49J27 Existence theories for problems in abstract spaces
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