Variational Inequalities and Surjectivity for Set-valued Monotone Mappings
نویسندگان
چکیده
We denote by σ(F,E) the topology on F generated by the family {ω(x, ε) : x ∈ E, ε > 0} as a subbase for the neighbourhood system at 0. It is easy to show that, if F possesses the σ(F,E)-topology, F becomes a locally convex topological vector space. The σ(E,F )-topology on E is defined analogously. A subset X of E is said to be σ(E,F )-compact if X is compact related to the σ(E,F )-topology. Let X be a nonempty subset of E. A set-valued mapping T : X → 2 is said to be monotone relative to the bilinear functional 〈 · , · 〉 : F ×E → Φ (monotone for short) if, for all x, y ∈ X, u ∈ T (x) and w ∈ T (y),
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