Affiliation:
1. Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran
2. Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
Abstract
It is known that the power function f (t) = t2 is not matrix monotone.
Recently, it has been shown that t2 preserves the order in some matrix
inequalities. We prove that if A = (A1,...,Ak) and B = (B1,...,Bk)
are k-tuples of positive matrices with 0 < m ? Ai; Bi ? M (i = 1,...,k)
for some positive real numbers m < M, then ?2 (A-11,...,A-1k) ?
(1+vk)2/4vk)2 ?-2(A1,...,Ak) and ?2 (A1+B1/2,..., Ak+Bk/2)?
(1+vk)2/4vk)2 ?2 (A1#B1,...Ak#Bk), where ? is a unital
positive multilinear mapping and v = M/m is the condition number of each Ai.
Publisher
National Library of Serbia
Cited by
2 articles.
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1. New inequalities for sector matrices applying Garg–Aujla inequalities;Advances in Operator Theory;2022-01-19
2. Some inequalities for positive multilinear mappings;Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics;2018-11-27