An order preserving inequality for three operators via furuta inequality

Furuta showed that if A ≥ B ≥ 0, then for each is decreasing for p ≥ t ≥ 0. Using this result, the following inequality is obtained for 0 < p ≤ 1, r ≥ 1, ¼ ≤ δ ≤ 1 and three positive operators A, B, C satisfy , , , .