... convex cone which is stable by product and composition of functions.Proof. Let f, g ∈Hand λ ≥ 0. First, it is clear that f λg, fg and the composition of functionsg ◦ f are nonnegative nondecreasing ... quasi-metric on E.2 Let ρ be a quasi-metric on E and γ a non-negative symmetric function on E × Esuch that γ ∼ ρ, then γ is a quasi-metric on E.3 Let ρ1 and ρ2be two quasimetrics on E, then ... of Inequalities and Applications 113.4. On the Operator −1/AAu on 0, 1 with u0u10Let A be a continuous function on 0, 1, which is positive and differentiable on 0, 1. Weassume...