Corrigendum for Vector Equilibrium Problems. Existence Theorems and Convexity of Solution Set

摘要

In the proof of E is contained in ∩ _(f∈C~#) T(f) of Theorem 3 of [1], there is a gap. Theorem 3 of [1] should reads as follows. THEOREM 3. Let X,Y,D and C be as in Theorem 1, and let C~# ≠ 0e. Let G, H: D × D → 2~Y be set-valued mappings satisfying the conditions (ⅰ)-(ⅵ) in Theorem 1. In addition, assume that G, H satisfy the following condition: (vii) for any fixed y ∈ D, G(., y) + H{., y): D → 2~Y is proper quasi-C-concave, i.e., for any x_1, x_2 ∈ D, t ∈ [0, 1], x = tx_1 + (1 - t)x_2, and for any w ∈ G(x, y) + H(x, y), there exists w_1 ∈ G(x_1, y) + H(x_1, y) or w_2 ∈ G(x_2, y) + H (x_2, y) such that w ∈ w_1+C or w ∈ w_2 + C.