Norm inequalities involving matrix monotone functions

Let A, B, X be complex matrices with A, B Hermitian positive definite and let f : (0, infinity) --> (0, infinity) be matrix monotone increasing. We prove (2 + t) \\\ A(1/2)(f(A)Xf(perpendicular to)(B) + f(perpendicular to)(A)Xf(B))B-1/2 \\\ less than or equal to 2 \\\ A(2)X + tAXB + XB2 \\\ and (2 + t) \\\ f(A)X + Xf(B) \\\ less than or equal to 2 f(lambda)/lambda \\\ A(3/2)XB(-1/2) + tA(1/2)XB(1/2) + A(-1/2)XB(3/2) \\\ where f(perpendicular to)(x) = x(f(x))(-1), t is an element of [-2,2] and lambda = min{sigma(A), sigma(B)}; sigma(A), sigma(B) being the spectrum of A, B respectively and \\\ . \\\ any unitarily invariant norm. These inequalities generalize Zhan's inequalities.