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Year 2019, Volume: 7 Issue: 1, 168 - 174, 15.04.2019

Abstract

References

  • [1] S. S. Dragomir, Some new reverses of Young’s operator inequality, Preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 130. [http://rgmia.org/papers/v18/v18a130.pdf].
  • [2] S. S. Dragomir, On new refinements and reverses of Young’s operator inequality, Preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 135. [http://rgmia.org/papers/v18/v18a135.pdf].
  • [3] S. S. Dragomir, Some inequalities for operator weighted geometric mean, Preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 139. [http://rgmia.org/papers/v18/v18a139.pdf ].
  • [4] S. S. Dragomir, Refinements and reverses of Holder-McCarthy operator inequality, Preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 143. [http://rgmia.org/papers/v18/v18a143.pdf].
  • [5] S. S. Dragomir, Some reverses and a refinement of H¨older operator inequality, Preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 147. [http://rgmia.org/papers/v18/v18a147.pdf].
  • [6] S. S. Dragomir, Some inequalities for Heinz operator mean, Preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 163. [Online http://rgmia.org/papers/v18/v18a163.pdf].
  • [7] S. S. Dragomir, Further inequalities for Heinz operator mean, Preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 167. [Online http://rgmia.org/papers/v18/v18a167.pdf].
  • [8] S. Furuichi, On refined Young inequalities and reverse inequalities, J. Math. Inequal. 5 (2011), 21-31.
  • [9] S. Furuichi, Refined Young inequalities with Specht’s ratio, J. Egyptian Math. Soc. 20 (2012), 46–49.
  • [10] F. Kittaneh and Y. Manasrah, Improved Young and Heinz inequalities for matrix, J. Math. Anal. Appl. 361 (2010), 262-269.
  • [11] F. Kittaneh and Y. Manasrah, Reverse Young and Heinz inequalities for matrices, Lin. Multilin. Alg., 59 (2011), 1031-1037.
  • [12] F. Kittaneh, M. Krnic, N. Lovricevic and J. Pecaric, Improved arithmetic-geometric and Heinz means inequalities for Hilbert space operators, Publ. Math. Debrecen, 2012, 80(3-4), 465–478.
  • [13] M. Krnic and J. Pecaric, Improved Heinz inequalities via the Jensen functional, Cent. Eur. J. Math. 11 (9) 2013,1698-1710.
  • [14] F. Kubo and T. Ando, Means of positive operators, Math. Ann. 264 (1980), 205–224.
  • [15] W. Liao, J. Wu and J. Zhao, New versions of reverse Young and Heinz mean inequalities with the Kantorovich constant, Taiwanese J. Math. 19 (2015), No. 2, pp. 467-479.
  • [16] W. Specht, Zer Theorie der elementaren Mittel, Math. Z. 74 (1960), pp. 91-98.
  • [17] M. Tominaga, Specht’s ratio in the Young inequality, Sci. Math. Japon., 55 (2002), 583-588.H.
  • [18] G. Zuo, G. Shi and M. Fujii, Refined Young inequality with Kantorovich constant, J. Math. Inequal., 5 (2011), 551-556.

Some Additive Inequalities for Heinz Operator Mean

Year 2019, Volume: 7 Issue: 1, 168 - 174, 15.04.2019

Abstract

In this paper we obtain some new additive inequalities for Heinz operator mean, namely the operator $H_{\nu }\left( A,B\right) :=\frac{1}{2}\left( A\sharp _{\nu }B+A\sharp _{1-\nu }B\right) $ where $A\sharp _{\nu }B:=A^{1/2}\left( A^{-1/2}BA^{-1/2}\right) ^{\nu }A^{1/2}$ is the weighted geometric mean for the positive invertible operators $A$ and $B,$ and $\nu \in \left[ 0,1\right] .$



References

  • [1] S. S. Dragomir, Some new reverses of Young’s operator inequality, Preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 130. [http://rgmia.org/papers/v18/v18a130.pdf].
  • [2] S. S. Dragomir, On new refinements and reverses of Young’s operator inequality, Preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 135. [http://rgmia.org/papers/v18/v18a135.pdf].
  • [3] S. S. Dragomir, Some inequalities for operator weighted geometric mean, Preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 139. [http://rgmia.org/papers/v18/v18a139.pdf ].
  • [4] S. S. Dragomir, Refinements and reverses of Holder-McCarthy operator inequality, Preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 143. [http://rgmia.org/papers/v18/v18a143.pdf].
  • [5] S. S. Dragomir, Some reverses and a refinement of H¨older operator inequality, Preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 147. [http://rgmia.org/papers/v18/v18a147.pdf].
  • [6] S. S. Dragomir, Some inequalities for Heinz operator mean, Preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 163. [Online http://rgmia.org/papers/v18/v18a163.pdf].
  • [7] S. S. Dragomir, Further inequalities for Heinz operator mean, Preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 167. [Online http://rgmia.org/papers/v18/v18a167.pdf].
  • [8] S. Furuichi, On refined Young inequalities and reverse inequalities, J. Math. Inequal. 5 (2011), 21-31.
  • [9] S. Furuichi, Refined Young inequalities with Specht’s ratio, J. Egyptian Math. Soc. 20 (2012), 46–49.
  • [10] F. Kittaneh and Y. Manasrah, Improved Young and Heinz inequalities for matrix, J. Math. Anal. Appl. 361 (2010), 262-269.
  • [11] F. Kittaneh and Y. Manasrah, Reverse Young and Heinz inequalities for matrices, Lin. Multilin. Alg., 59 (2011), 1031-1037.
  • [12] F. Kittaneh, M. Krnic, N. Lovricevic and J. Pecaric, Improved arithmetic-geometric and Heinz means inequalities for Hilbert space operators, Publ. Math. Debrecen, 2012, 80(3-4), 465–478.
  • [13] M. Krnic and J. Pecaric, Improved Heinz inequalities via the Jensen functional, Cent. Eur. J. Math. 11 (9) 2013,1698-1710.
  • [14] F. Kubo and T. Ando, Means of positive operators, Math. Ann. 264 (1980), 205–224.
  • [15] W. Liao, J. Wu and J. Zhao, New versions of reverse Young and Heinz mean inequalities with the Kantorovich constant, Taiwanese J. Math. 19 (2015), No. 2, pp. 467-479.
  • [16] W. Specht, Zer Theorie der elementaren Mittel, Math. Z. 74 (1960), pp. 91-98.
  • [17] M. Tominaga, Specht’s ratio in the Young inequality, Sci. Math. Japon., 55 (2002), 583-588.H.
  • [18] G. Zuo, G. Shi and M. Fujii, Refined Young inequality with Kantorovich constant, J. Math. Inequal., 5 (2011), 551-556.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Sever DRAGOMİR

Publication Date April 15, 2019
Submission Date April 24, 2018
Acceptance Date December 20, 2018
Published in Issue Year 2019 Volume: 7 Issue: 1

Cite

APA DRAGOMİR, S. (2019). Some Additive Inequalities for Heinz Operator Mean. Konuralp Journal of Mathematics, 7(1), 168-174.
AMA DRAGOMİR S. Some Additive Inequalities for Heinz Operator Mean. Konuralp J. Math. April 2019;7(1):168-174.
Chicago DRAGOMİR, Sever. “Some Additive Inequalities for Heinz Operator Mean”. Konuralp Journal of Mathematics 7, no. 1 (April 2019): 168-74.
EndNote DRAGOMİR S (April 1, 2019) Some Additive Inequalities for Heinz Operator Mean. Konuralp Journal of Mathematics 7 1 168–174.
IEEE S. DRAGOMİR, “Some Additive Inequalities for Heinz Operator Mean”, Konuralp J. Math., vol. 7, no. 1, pp. 168–174, 2019.
ISNAD DRAGOMİR, Sever. “Some Additive Inequalities for Heinz Operator Mean”. Konuralp Journal of Mathematics 7/1 (April 2019), 168-174.
JAMA DRAGOMİR S. Some Additive Inequalities for Heinz Operator Mean. Konuralp J. Math. 2019;7:168–174.
MLA DRAGOMİR, Sever. “Some Additive Inequalities for Heinz Operator Mean”. Konuralp Journal of Mathematics, vol. 7, no. 1, 2019, pp. 168-74.
Vancouver DRAGOMİR S. Some Additive Inequalities for Heinz Operator Mean. Konuralp J. Math. 2019;7(1):168-74.
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