On an Inequality of J.L. Brenner.

Let p, q, s, and t be positive real numbers, and let k be a nonnegative integer with p + q ≤ 1, s > k + 1, and t > k + 1. We prove that if [formula] then Ak(Ps, t) + Ak(qt, s) > 1 + Ak((p + q)m, M),(∗) where m = min(s, t) and M = max(s, t). Inequality (∗) sharpens and extends a result of J. L. Brenner.