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Quadratic refinements of Young type inequalities

In: Mathematica Slovaca, vol. 70, no. 5
Yonghui Ren - Pengtong Li - Guoqing Hong

Details:

Year, pages: 2020, 1087 - 1096
Keywords:
Young’s inequality, operator inequality, unitarily invariant norms
About article:
In this paper, we mainly give some quadratic refinements of Young type inequalities. Namely: \[ (va+(1-v)b)2-v{{∑\limitsj=1N}}2j\Big(b- \sqrt[2j]{ab2j-1} \Big)2≤(avb1-v)2+v2(a-b)2 \] for $v \not\in[0,((1) / (2N+1))],$ $N\in \mathbb{N}, a,b>0;$ and \[ (va+(1-v)b)2-(1-v){{∑\limitsj=1N}}2j\Big(a- \sqrt[2j]{a2j-1b} \Big)2≤(avb1-v)2+(1-v)2(a-b)2 \] for $ v \not\in[1-((1) / (2N+1)),1],$ $N\in \mathbb{N}, a,b>0.$ As an application of these scalars results, we obtain some matrix inequalities for operators and Hilbert-Schmidt norms.
How to cite:
ISO 690:
Ren, Y., Li, P., Hong, G. 2020. Quadratic refinements of Young type inequalities. In Mathematica Slovaca, vol. 70, no.5, pp. 1087-1096. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0416

APA:
Ren, Y., Li, P., Hong, G. (2020). Quadratic refinements of Young type inequalities. Mathematica Slovaca, 70(5), 1087-1096. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0416
About edition:
Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Published: 27. 9. 2020