Linear and Multilinear Algebra, ( ISI ), Volume (64), No (12), Year (2016-12) , Pages (2463-2473)

Title : ( A New Class of Operator Monotone Functions via Operator Means )

Authors: Rajinder Pal , Mandeep Singh , Mohammad Sal Moslehian , Jaspal Singh Aujla ,

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Abstract

In this paper, we obtain a new class of functions, which is developed via the Hermite--Hadamard inequality for convex functions. The well-known one-one correspondence between the class of operator monotone functions and operator connections declares that the obtained class represents the weighted logarithmic means. We shall also consider weighted identric mean and some relationships between various operator means. Among many things, we extended the weighted arithmetic--geometric operator mean inequality as $A\#_{t}B\leq A\ell_t B\leq \frac{1}{2}(A\#_{t}B + A\nabla_{t} B)\le A\nabla_tB$ and $A\#_{t}B\leq A\mathcal{I}_t B\leq A\nabla_{t} B$ involving the considered operator means.

Keywords

Operator monotone function; positive operator; positive operator; operator mean; invariance of mean
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@article{paperid:1055615,
author = {Rajinder Pal and Mandeep Singh and Sal Moslehian, Mohammad and Jaspal Singh Aujla},
title = {A New Class of Operator Monotone Functions via Operator Means},
journal = {Linear and Multilinear Algebra},
year = {2016},
volume = {64},
number = {12},
month = {December},
issn = {0308-1087},
pages = {2463--2473},
numpages = {10},
keywords = {Operator monotone function; positive operator; positive operator; operator mean; invariance of mean},
}

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%0 Journal Article
%T A New Class of Operator Monotone Functions via Operator Means
%A Rajinder Pal
%A Mandeep Singh
%A Sal Moslehian, Mohammad
%A Jaspal Singh Aujla
%J Linear and Multilinear Algebra
%@ 0308-1087
%D 2016

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