Electronic Journal of Linear Algebra, ( ISI ), Volume (26), Year (2013-8) , Pages (742-753)

Title : ( Refinements of the operator Jensen-Mercer inequality )

Authors: Mohsen Kian , Mohammad Sal Moslehian ,

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We present a Hermite--Hadamard--Mercer type inequality and then generalize it for Hilbert space operators. We also prove f left(M+m- sum_{i=1}^{n}x_iA_i right) leq f(M)+f(m)- sum_{i=1}^{n}f(x_i)A_i , where f is a convex function on an interval [m,M] containing 0 , x_i in[m,M] , i=1, cdots,n and A_i are positive operators acting on a finite dimensional Hilbert space whose sum is equal to the identity operator. We also establish a Jensen--Mercer operator type inequality for separately operator convex functions.


, Jensen--Mercer inequality, Operator convex, Jensen inequality, Hermite--Hadamard inequality, jointly operator convex
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author = {Mohsen Kian and Sal Moslehian, Mohammad},
title = {Refinements of the operator Jensen-Mercer inequality},
journal = {Electronic Journal of Linear Algebra},
year = {2013},
volume = {26},
month = {August},
issn = {1537-9582},
pages = {742--753},
numpages = {11},
keywords = {Jensen--Mercer inequality; Operator convex; Jensen inequality; Hermite--Hadamard inequality; jointly operator convex},


%0 Journal Article
%T Refinements of the operator Jensen-Mercer inequality
%A Mohsen Kian
%A Sal Moslehian, Mohammad
%J Electronic Journal of Linear Algebra
%@ 1537-9582
%D 2013