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December 2020 Some inequalities for weighted and integral means of operator convex functions
Silvestru Sever Dragomir
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SUT J. Math. 56(2): 109-127 (December 2020). DOI: 10.55937/sut/1609966712


Let f be an operator convex function on I and A,B ϵ SAI(H), the convex set of selfadjoint operators with spectra in I. If AB and f, as an operator function, is Gâteaux differentiable on

[A,B] := {(1t)A+tB|t[0,1]},

while p : [0,1][0, ) is Lebesgue integrable satisfying the condition

00τp(s)ds01p(s)ds for all τ[0,1]

and symmetric, namely p(1t) =p(t) for all tϵ [0, 1] then


Some particular examples of interest are also given.


The author would like to thank the anonymous referee for valuable suggestions that have been implemented in the final version of the paper.


Download Citation

Silvestru Sever Dragomir. "Some inequalities for weighted and integral means of operator convex functions." SUT J. Math. 56 (2) 109 - 127, December 2020.


Received: 5 February 2020; Published: December 2020
First available in Project Euclid: 8 June 2022

Digital Object Identifier: 10.55937/sut/1609966712

Primary: 47A63 , 47A99

Keywords: Féjer’s inequalities , Hermite-Hadamard inequality , integral inequalities , operator convex functions

Rights: Copyright © 2020 Tokyo University of Science

Vol.56 • No. 2 • December 2020
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