On BVPs in l∞(A)

Let A 6 = ∅ be a set, and let l∞(A) denote the real Banach space of all bounded functions x = (xα)α∈A: A → R, endowed with the supremum norm | | · ||. Let l∞(A) be ordered by the cone K = {x: xα ≥ 0 (α ∈ A)}