SPECHT'S RATIO IN THE YOUNG INEQUALITY

By M. Tominaga. 2002

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Alternative reverse inequalities for Young's inequality (2011, methodology): “e real number h. Note that limh→1S(h) = 1 and S(h) = S(1/h) > 1 for h 6= 1 ,h > 0. We call the inequality (2) a ratio-type reverse inequalitiy for Young’s inequality. M. Tominaga also showed in [11] the following inequality: (1 −λ)a +λb ≤ L(a,b)logS a b +a1−λbλ, (3) for positive real numbers ”
REFINED YOUNG INEQUALITY WITH KANTOROVICH CONSTANT (2011, methodology): “The inequality (1) is also called a weighted arithmetic-geometric mean inequality and its reverse inequality was given in [10] with the Specht ratio as follows: a∇μb S(h)a1−μbμ (2)”
Refined Young inequalities with Specht's ratio (2010, methodology): “an and operator inequality 2000 Mathematics Subject Classiﬁcation : 15A45 and 47A63 1 Introduction We start from the famous Young inequality: (1 −ν)a+νb ≥ a1−νbν (1) for positive numbers a, b and ν ∈ [0,1]. The inequality (1) is also called ν-weighted arithmeticgeometric mean inequality and its reve”
NEW VERSIONS OF REVERSE YOUNG AND HEINZ MEAN INEQUALITIES WITH THE KANTOROVICH CONSTANT (2015, background): “Tominaga [8] had proved a reverse Young inequality with the Specht’s ratio”