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Some improvements of the Young mean inequality and its reverse

In: Mathematica Slovaca, vol. 68, no. 4
Maryam Khosravi
Detaily:
Rok, strany: 2018, 803 - 810
Kľúčové slová:
weighted arithmetic and geometric mean, Heinz mean, strictly positive operator, Young inequality, Kantorovich constant
O článku:
The main objective of the present paper, is to obtain some new versions of Young-type inequalities with respect to two weighted arithmetic and geometric means and their reverses, using two inequalities

$$K\Big(((b) / (a)),2\Big)r≤((a\nablaνb) / (a\sharpνb))≤ K\Big(((b) / (a)),2\Big)R,$$

where $r=\min\{ν,1-ν\}$, $R=\max\{ν,1-ν\}$ and $K(t,2)=(((t+1)2) / (4t))$ is the Kantorovich constant, and

$$e(h-1,ν)≤((a\nablaνb) / (a\sharpνb))≤ e(h,ν),$$

where $h=\max\{((a) / (b)),((b) / (a))\}$ and $e(t,ν)=\exp(4{ν(1-ν)}(K(t,2)-1)(1-((1) / (2t))))$. Also some operator versions of these inequalities and some inequalities related to Heinz mean are proved.
Ako citovať:
ISO 690:
Khosravi, M. 2018. Some improvements of the Young mean inequality and its reverse. In Mathematica Slovaca, vol. 68, no.4, pp. 803-810. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0146

APA:
Khosravi, M. (2018). Some improvements of the Young mean inequality and its reverse. Mathematica Slovaca, 68(4), 803-810. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0146
O vydaní:
Publikované: 10. 8. 2018