Improved Young and Heinz inequalities for matrices

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Reverse Young and Heinz inequalities for matrices (2011, background): “In our recent work [6] we gave a refinement of (1.”
Alternative reverse inequalities for Young's inequality (2011, methodology): “sitive operator 2000 Mathematics Subject Classiﬁcation : 15A39 and 15A45 1 Introduction It is well known the Young inequality a1−λbλ ≤ (1 −λ)a+λb, (1) for positive real numbers a,b and λ ∈ [0,1]. See [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] for improvements of Young’s inequality and their recent advances. On”
Young-type inequalities and their matrix analogues (2015, methodology): “11) and inequalities similar to the ones obtained in [3,4] based in [10].”
On the Convexity of the Heinz Means (2010, methodology): “For the special case p = 2, which corresponds to the Hilbert‐Schmidt norm, this result has been inferred in [ 7 ] using the improved Heinz inequality”
Improvements of Berezin number inequalities (2018, unknown): “A refinement of the Young inequality is presented in [17] as follows: aαb1−α ≤ αa + (1 − α)b − r0(a − b1/2)2, (2.”
REFINED YOUNG INEQUALITY WITH KANTOROVICH CONSTANT (2011, background): “See also [5] for another type of improvement for the classical Young inequality.”