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Zbl 1014.49007
Cho, Y.J.; Kim, J.K.; Verma, Ram U.
A class of nonlinear variational inequalities involving partially relaxed monotone mappings and general auxiliary problem principle. (English)
[J] Dyn. Syst. Appl. 11, No.3, 333-337 (2002). ISSN 1056-2176

Summary: The approximation solvability of the following class of nonlinear variational inequality problems based on the general auxiliary problem principle is discussed: Find an element $x^*\in K$ such that $$\langle T(x^*),x-x^*\rangle + f(x)-f(x^*)\geq 0$$ for all $x\in K$, where $T:K\to E^*$ is a mapping from a nonempty closed convex subset $K$ of a reflexive Banach space $E$ into its dual $E^*$ and $f:K\to R$ is a continuous convex functional on $K$.

MSC 2000:: *49J40 Variational methods including variational inequalities

Keywords: nonlinear variational inequality; general auxiliary problem principle

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