Alternative reverse inequalities for Young's inequality

Abstract

Two reverse inequalities for Young's inequality were shown by M. Tominaga, using Specht ratio. In this short paper, we show alternative reverse inequalities for Young's inequality without using Specht ratio.

Some inequalities on generalized entropies

“…On the other hand, the studies on refinements for Young's inequality have given a great progress in the papers [18,19,20,21,22,23,24,25,26,27,28,29]. In the present paper, we give some inequalities on the Tsallis entropies applying two type inequalities obtained in [23,26].…”

A novel stability theorem about fractional nonlinear systems with time-delay

“…That is, when α < 1, if any eigenvalue λ of Jacobian matrix J(x) satisfies Re(λ) ≤ 0 for any x(t), fractional nonlinear system (3) is also stable to zero. Lemma 2 [23] Young's inequality: For any vectors x(t), y(t) ∈ R n , and any η > 0, the following matrix inequality holds:…”

Local extreme points and a Young-type inequality

“…The following inequality is a refinement of the lefthand side of a refinement of the inequality of Young proved in 2010 and 2011 by Kittaneh and Manasrah in [12], [13]. Many generalizations and refinements of Young's inequality are presented also in [10], [8], [9] and references therein.…”