Weighted arithmetic-geometric operator mean inequalities

In this paper, we refine and generalize some weighted arithmetic-geometric operator mean inequalities due to Lin (Stud. Math. 215:187-194, 2013) and Zhang (Banach J. Math. Anal. 9:166-172, 2015) as follows: Let A and B be positive operators. If 0 < m <= A <= m' <= M' <= B <= M or 0 < m <= B <= m' < M' <= A <= M, then for a positive unital linear map phi, phi(2)(A del B-alpha) <= [K(h)/S(h '')](2) phi(2)(A#B-alpha), phi(2)(A del B-alpha) <= [K(h)/S(h '')](2) [phi(A)#(alpha)phi(B)](2), phi(2)(A del B-alpha)<= 1/16[K-2(h)(M(2+)m(2))/S-2(h '')M(2)m(2)](p) phi(2p)(A#B-alpha), phi(2p)(A del B-alpha)<= 1/16[K-2(h)(M-2+m(2))(2)/S-2(h '')M(2)m(2)]p [phi(A)#(alpha)phi(B)](2p), where alpha epsilon [0,1], K(h) = (h+1)(2)/4h, S(h')= h'1/h'-1/e log h' 1/h'-1, h=M/m, h' = M'/m', r = min{alpha, 1-alpha} and p >= 2.