and Applied Analysis 3 (ii) The scalar C-pseudomonotonicity in Definition 2 is weaker than C-pseudomonotonicity in Definition 1(ii). In fact, for any ξ ∈ C∗ \ {0}, x, y ∈ X, if ⟨ξ(u∗), y − x⟩ ≥ 0, then we have ⟨u∗, y − x⟩ ∉ − intC. Then, it follows from the Cpseudomonotonicity of T that ⟨V∗, y − x⟩ ∈ C, which implies that ⟨ξ(V∗), y − x⟩ ≥ 0. Definition 5. The topological space E is said to be c...