Reverses of Féjer s Inequalities for Convex Functions

Let f be a convex function on I and a, b ∈ I with a b. If p : [a, b] → [0,∞) is Lebesgue integrable and symmetric, namely p (b + a − t) = p (t) for all t ∈ [a, b] , then we show in this paper that [Mathematical formula]