Geodesic
Some results of reverses Young's inequalities
Filomat, Tome 36 (2022) no. 8, p. 2541

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In this paper, we present some refinements of reverse Young's inequalities. Among other results, a refinement of reverse operator Young inequalities says A∇ v B + 2λ(A∇B − A♯B) ≤ m∇ λ M m♯ λ M A♯ v B, where 0 mI ≤ A, B ≤ MI, λ = min{v, 1 − v} and v ∈ [0, 1], extending a key result in [J. Math. Anal. Appl. 465 (2018) 267-280] and [Linear Multilinear Algebra 67 (2019) 1567-1578]. Furthermore, we give a reverse of Young's inequalities due to [Math. Slovaca 70 (2020), 453-466]. Moreover, we give a generalization of reverse Young-type inequality, and we also show a new Young-type inequality which is either better or not uniformly better than the main results in [Rocky Mountain J. Math. 46 (2016), 1089-1105]. As applications of these results, we obtain some inequalities for operators, Hilbert-Schmidt norms, unitarily invariant norms and determinants.
DOI : 10.2298/FIL2208541R
Classification : 15A60, 47A30, 47A60
Keywords: Young’s inequality, Hilbert-Schmidt norms, Determinant, Unitarily invariant norms 
Yonghui Ren; Pengtong Li. Some results of reverses Young's inequalities. Filomat, Tome 36 (2022) no. 8, p. 2541 . doi: 10.2298/FIL2208541R
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     title = {Some results of reverses {Young's} inequalities},
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     doi = {10.2298/FIL2208541R},
     language = {en},
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