Abstract: | Let A, B, and X be bounded linear operators on a complex separable Hilbert space. It is shown that if A and B are self-adjoint with and for some real numbers a 1, a 2, b 1, and b 2, then for every unitarily invariant norm|||·|||, . If, in addition, X is positive, then . These norm inequalities generalize recent related inequalities due to Kittaneh, Bhatia-Kittaneh, and Wang-Du. |