Bounds for the ratios of differences of power means in two arguments

Kouba, Omran

doi:10.7153/mia-17-66

Cited by 3 publications

(4 citation statements)

References 5 publications

(13 reference statements)

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“…and again using the results in [21] it is proved that the sharp lower bound for the last expression is 4 p−1 .…”

Section: Triangle Inequality In the Entropy-transport Casementioning

confidence: 84%

“…If 1 < p < 3 2 one needs precise bounds that I have found in [21]. The supremum of the left hand side of (137) is 4 p−1 .…”

Section: Triangle Inequality In the Entropy-transport Casementioning

confidence: 99%

“…Case s ≤ r The strategy is to use again Lemma 13 and the triangle inequality for the case p = 1, but I have to derive a different inequality with respect to the previous step. If 1 < p < 3 2 one needs precise bounds that I have found in [21]. The supremum of the left hand side of (137) is 4 p−1 .…”

Section: Triangle Inequality In the Entropy-transport Casementioning

confidence: 99%

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Metric Properties of Homogeneous and Spatially Inhomogeneous $F$ -Divergences

Ponti

2020

IEEE Trans. Inform. Theory

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In this paper I investigate the construction and the properties of the so-called marginal perspective cost H, a function related to Optimal Entropy-Transport problems obtained by a minimizing procedure, involving a cost function c and an entropy function. In the pure entropic case, which corresponds to the choice c = 0, the function H naturally produces a symmetric divergence. I consider various examples of entropies and I compute the induced marginal perspective function, which includes some well-known functionals like the Hellinger distance, the Jensen-Shannon divergence and the Kullback-Liebler divergence. I discuss the metric properties of these functions and I highlight the important role of the so-called Matusita divergences. In the entropy-transport case, starting from the power like entropy Fp(s) = (s p − p(s − 1) − 1)/(p(p − 1)) and the cost c = d 2 for a given metric d, the main result of the paper ensures that for every p > 1 the induced marginal perspective cost Hp is the square of a metric on the corresponding cone space.

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“…and again using the results in [21] it is proved that the sharp lower bound for the last expression is 4 p−1 .…”

Section: Triangle Inequality In the Entropy-transport Casementioning

confidence: 84%

“…If 1 < p < 3 2 one needs precise bounds that I have found in [21]. The supremum of the left hand side of (137) is 4 p−1 .…”

Section: Triangle Inequality In the Entropy-transport Casementioning

confidence: 99%

See 1 more Smart Citation

Metric Properties of Homogeneous and Spatially Inhomogeneous $F$ -Divergences

Ponti

2020

IEEE Trans. Inform. Theory

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show abstract

“…For example, in [9], Ibrahim and Dragomir established inequalities by utilizing power series and Young's inequality. In [10], Kouba used classical analysis to obtain some new inequalities. In [12], V. Mascioni discover new inequalities by the differences of some Stolarsky means.…”

Section: Introductionmentioning

confidence: 99%