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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 68, Issue 4

Issues

Some improvements of the young mean inequality and its reverse

Maryam Khosravi
  • Department of Pure Mathematics Faculty of Mathematics and Computer Shahid Bahonar University of Kerman, Kerman, Iran
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Published Online: 2018-08-06 | DOI: https://doi.org/10.1515/ms-2017-0146

Abstract

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(ba,2)raνbaνbK(ba,2)R,

where r = min{ν, 1 – ν}, R = max{ν,1 – ν} and K(t,2) = (t+1)24t is the Kantorovich constant, and

e(h1,ν)aνbaνbe(h,ν),

where h = max {ab,ba} and e(t,ν) = exp (4ν(1 – ν)(K(t,2)–1) (112t)). Also some operator versions of these inequalities and some inequalities related to Heinz mean are proved.

MSC 2010: Primary 47A63; Secondary 47A64; 47B65

Keywords: weighted arithmetic and geometric mean; Heinz mean; strictly positive operator; Young inequality; Kantorovich constant

References

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    Bakherad, M.—Krnic, M.—Moslehian, M. S.: Reverses of the Young inequality for matrices and operators, Rocky Mountain J. Math. 46 (2016), 1089–1105.CrossrefGoogle Scholar

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About the article

Received: 2016-10-04

Accepted: 2017-01-14

Published Online: 2018-08-06

Published in Print: 2018-08-28


Communicated by Werner Timmermann


Citation Information: Mathematica Slovaca, Volume 68, Issue 4, Pages 803–810, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0146.

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