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A perturbed algorithm for strongly nonlinear variational-like inclusions. (English) Zbl 0979.49008

A generalized \(\eta\)-subdifferential is defined, and applied to solvability of a strongly nonlinear variational-like inclusion with a nonlinear operator \(T\): \[ (\forall y\in H)\quad \langle T(x)- A(x), \eta(y,x)\rangle\geq \varphi(x)- \varphi(y). \] Conditions are found for convergence of a perturbed iterative algorithm to a solution, assuming monotone and other properties of \(T\) and \(\eta\), and inequalities on Lipschitz constants.

MSC:

49J40 Variational inequalities
47J20 Variational and other types of inequalities involving nonlinear operators (general)
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