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Research Article

Further inequalities involving the weighted geometric operator mean and the Heinz operator mean

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Pages 4432-4454 | Received 16 Jan 2020, Accepted 22 Jan 2021, Published online: 09 Feb 2021

References

  • Ando T, Li CK, Mathias R. Geometric means. Linear Algebra Appl. 2004;38:305–334.
  • Atteia M, Raïssouli M. Self dual operators on convex functionals, geometric mean and square root of convex functionals. J Convex Anal. 2001;8:223–240.
  • Kubo F, Ando T. Means of positive linear operators. Math Ann. 1980;246:205–224.
  • Raïssouli M, Moslehian MS, Furuichi S. Relative entropy and Tsallis entropy of two accretive operators. C R Acad Sci Paris, Ser I. 2017;355:687–693.
  • Kittaneh F, Moslehian MS, Sababheh M. Quadratic interpolation of the Heinz mean. Math Inequal Appl. 2018;21/3:739–757. Available from: http://dx.doi.org/10.7153/mia-2018-21-53.
  • Raïssouli M. Functional versions of some refined and reversed operator mean-inequalities. Bull Austr Math Soc. 2017;96/3:496–503. Available from: http://dx.doi.org/10.1017/s0004972717000594.
  • Fujii JI, Seo Y. Tsallis relative operator entropy with negative parameters. Adv Oper Theory. 2016;1:219–235.
  • Furuichi S, Yanagi K, Kuriyama K. A note on operator inequalities of Tsallis relative operator entropy. Linear Algebra Appl. 2005;407:19–31.
  • Furuta T. Parametric extensions of Shannon inequality and its reverse one in Hilbert space operators. Linear Algebra Appl. 2004;381:219–235.
  • Fujii JI, Kamei E. Relative operator entropy in noncommutative information theory. Math Jpn. 1989;34:341–348.
  • Furuichi S. Inequalities for Tsallis relative entropy and generalized skew information. Linear Multilinear Algebra. 2011;59(10):1143–1158.
  • Furuichi S, Minculete N. Inequalities for relative operator entropies and operator means. Acta Math Vietnam. 2018;43(4):607–618. https://doi.org/10.1007/s40306-018-0250-7.
  • Raïssouli M, Furuichi S. Functional version for Furuta parametric relative operator entropy. J Inequal Appl. 2018;2018:212.
  • Raïssouli M, Furuichi S. Some inequalities involving Heron and Heinz means of two convex functionals. 19 Dec 2018. To appear in Analysis Mathematica. Available from: http:arXiv:1809.01820v2 [math.FA]
  • Zou L. Operator inequalities associated with Tsallis relative operator entropy. Math Ineq Appl. 2015;18/2:401–406.
  • Dragomir SS, Agarwal RP, Barnett NS. Inequalities for beta and gamma functions via some classical and new integral inequalities. J Inequal Appl. 2000;5:103–165.
  • Raïssouli M. United explicit form for a game of monotone and chaotic matrix means. Int Electron J Pure Appl Math. 2010;1/4:475–493.
  • Guo C-H. On Newton's method and Halley's method for the principal pth root of a matrix. Linear Alg Appl. 2010;432:1905–1922.
  • Higham NJ. Newton's method for the matrix square root. Math Comput. 1986;46/174:537–549.
  • Iannazzo B. On the Newton method for the matrix pth root. SIAM J Matrix and Appl. 2006;28:503–523.
  • Petković M, Petković LD. Families of optimal multipoint methods for solving nonlinear equations: a survey. Appl Anal Discrete Math. 2010;4:1–22.
  • Fassi M, Iannazo B. Computing the weighted geometric mean of two large-scale matrices and its inverse times a vector. 2016. Available from: http://eprints.maths.manchester.ac.uk/
  • Raïssouli M, Leazizi F, Chergui M. Arithmetico-geometrico-harmonic mean of three positive operators. J Inequal Pure Appl Math. 2009;10/4: Art. 117.
  • Iannazzo B. The geometric mean of two matrices from a computational viewpoint. Num Linear Alg Appl. 2016;23/2:208–229.
  • Raïssouli M, Leazizi F. Continued fraction expansion of the geometric matrix mean and applications. Linear Alg Appl. 2003;359:37–57.

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