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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

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1572-9176
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Further refinements of generalized numerical radius inequalities for Hilbert space operators

Monire Hajmohamadi / Rahmatollah Lashkaripour
  • Corresponding author
  • Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
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/ Mojtaba Bakherad
Published Online: 2019-05-07 | DOI: https://doi.org/10.1515/gmj-2019-2023

Abstract

In this paper, we show some refinements of generalized numerical radius inequalities involving the Young and Heinz inequality. In particular, we present

wpp(A1*T1B1,,An*TnBn)n1-1r21ri=1n[Bi*f2(|Ti|)Bi]rp+[Ai*g2(|Ti*|)Ai]rp1r-infx=1η(x),

where Ti,Ai,Bi𝔹() (1in), f and g are nonnegative continuous functions on [0,) satisfying f(t)g(t)=t for all t[0,), p,r1, N, and

η(x)=12i=1nj=1N((Ai*g2(|Ti*|)Ai)px,x2j-1-kj(Bi*f2(|Ti|)Bi)px,xkj2j-(Bi*f2(|Ti|)Bi)px,xkj+1(Ai*g2(|Ti*|)Ai)px,x2j-1-kj-12j)2.

Keywords: Euclidean operator radius; Heinz means; numerical radius; positive operator; Young inequality

MSC 2010: 47A12; 47A63; 47A30

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About the article

Received: 2016-09-29

Accepted: 2018-05-21

Published Online: 2019-05-07


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2019-2023.

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