... More matrix forms of the arithmeticgeometric mean in-equality. SIAM J. Matrix Anal. Appl. 14, 132–136 (1993)2. Kittaneh, F: On the convexity of the Heinz means. Integ. Equ. Oper. Theory68, 519–527 ... on the interval [a, b]. Thenfa + b2≤1b − abaf(t)dt ≤f(a) + f( b)2.In [2], Kittaneh obtained several refinements of the Heinz inequalities byusing the previous lemma. In the ... distribution, and reproduction in any medium, provided the original work is properly cited.1Refinements of the Heinz inequalitiesYuming FengSchool of Mathematics and Statistics, Chongqing Three Gorges...