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We prove a new vectorial functional inequality of Poincaré Beckner type.
This asymptotic behaviour is related to a functional inequality, which links the distance with its dissipation and ensures a spectral gap in Wasserstein distance.
Then satisfies the functional inequality (3.48).
and the Cauchy-Jensen additive functional inequality.
Then f satisfies the functional inequality (4.5).
Assume that a mapping satisfies the functional inequality (32).
It also appears in a certain functional inequality (cf. [9]).
If a mapping with satisfies the functional inequality (21).
for all We consider the following functional inequality: (32).
Assume that a mapping with satisfies the functional inequality (318).
Gilányi [34] showed that if satisfies the functional inequality.
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