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Additive Refinements and Reverses of Young's Operator Inequality Via a Result of Cartwright and Field

Year 2021, , 1 - 8, 22.03.2021
https://doi.org/10.32323/ujma.833414

Abstract

In this paper we obtain some new additive refinements and reverses of Young's operator inequality via a result of Cartwright and Field. Comparison with other additive Young's type inequalities are also provided.

References

  • [1] D.I. Cartwright, M.J. Field, A refinement of the arithmetic mean-geometric mean inequality, Proc. Amer. Math. Soc., 71 (1978), 36-38.
  • [2] 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].
  • [3] 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].
  • [4] 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 ].
  • [5] S.S. Dragomir, Refinements and reverses of H¨older-McCarthy operator inequality, Preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 143. [http://rgmia.org/papers/v18/v18a143.pdf].
  • [6] 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].
  • [7] S. Furuichi, Refined Young inequalities with Specht’s ratio, J. Egyptian Math. Soc. 20(2012), 46-49.
  • [8] S. Furuichi, On refined Young inequalities and reverse inequalities, J. Math. Inequal. 5 (2011), 21-31.
  • [9] F. Kittaneh, Y. Manasrah, Improved Young and Heinz inequalities for matrix, J. Math. Anal. Appl., 361 (2010), 262-269
  • [10] F. Kittaneh, Y. Manasrah, Reverse Young and Heinz inequalities for matrices, Linear Multilinear Algebra., 59 (2011), 1031-1037.
  • [11] W. Liao, J. Wu, J. Zhao, New versions of reverse Young and Heinz mean inequalities with the Kantorovich constant, Taiwanese J. Math. 19(2) (2015), 467-479.
  • [12] N. Minculete, S. Furuichi, Several applications of Cartwright-Field’s inequality, Int. J. Pure Appl. Math., 71(1) (21), 19-30.
  • [13] M. Tominaga, Specht’s ratio in the Young inequality, Sci. Math. Japon., 55 (2002), 583-588.
  • [14] G. Zuo, G. Shi, M. Fujii, Refined Young inequality with Kantorovich constant, J. Math. Inequal., 5 (2011), 551-556.
Year 2021, , 1 - 8, 22.03.2021
https://doi.org/10.32323/ujma.833414

Abstract

References

  • [1] D.I. Cartwright, M.J. Field, A refinement of the arithmetic mean-geometric mean inequality, Proc. Amer. Math. Soc., 71 (1978), 36-38.
  • [2] 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].
  • [3] 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].
  • [4] 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 ].
  • [5] S.S. Dragomir, Refinements and reverses of H¨older-McCarthy operator inequality, Preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 143. [http://rgmia.org/papers/v18/v18a143.pdf].
  • [6] 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].
  • [7] S. Furuichi, Refined Young inequalities with Specht’s ratio, J. Egyptian Math. Soc. 20(2012), 46-49.
  • [8] S. Furuichi, On refined Young inequalities and reverse inequalities, J. Math. Inequal. 5 (2011), 21-31.
  • [9] F. Kittaneh, Y. Manasrah, Improved Young and Heinz inequalities for matrix, J. Math. Anal. Appl., 361 (2010), 262-269
  • [10] F. Kittaneh, Y. Manasrah, Reverse Young and Heinz inequalities for matrices, Linear Multilinear Algebra., 59 (2011), 1031-1037.
  • [11] W. Liao, J. Wu, J. Zhao, New versions of reverse Young and Heinz mean inequalities with the Kantorovich constant, Taiwanese J. Math. 19(2) (2015), 467-479.
  • [12] N. Minculete, S. Furuichi, Several applications of Cartwright-Field’s inequality, Int. J. Pure Appl. Math., 71(1) (21), 19-30.
  • [13] M. Tominaga, Specht’s ratio in the Young inequality, Sci. Math. Japon., 55 (2002), 583-588.
  • [14] G. Zuo, G. Shi, M. Fujii, Refined Young inequality with Kantorovich constant, J. Math. Inequal., 5 (2011), 551-556.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Sever Dragomır

Publication Date March 22, 2021
Submission Date November 30, 2020
Acceptance Date March 1, 2021
Published in Issue Year 2021

Cite

APA Dragomır, S. (2021). Additive Refinements and Reverses of Young’s Operator Inequality Via a Result of Cartwright and Field. Universal Journal of Mathematics and Applications, 4(1), 1-8. https://doi.org/10.32323/ujma.833414
AMA Dragomır S. Additive Refinements and Reverses of Young’s Operator Inequality Via a Result of Cartwright and Field. Univ. J. Math. Appl. March 2021;4(1):1-8. doi:10.32323/ujma.833414
Chicago Dragomır, Sever. “Additive Refinements and Reverses of Young’s Operator Inequality Via a Result of Cartwright and Field”. Universal Journal of Mathematics and Applications 4, no. 1 (March 2021): 1-8. https://doi.org/10.32323/ujma.833414.
EndNote Dragomır S (March 1, 2021) Additive Refinements and Reverses of Young’s Operator Inequality Via a Result of Cartwright and Field. Universal Journal of Mathematics and Applications 4 1 1–8.
IEEE S. Dragomır, “Additive Refinements and Reverses of Young’s Operator Inequality Via a Result of Cartwright and Field”, Univ. J. Math. Appl., vol. 4, no. 1, pp. 1–8, 2021, doi: 10.32323/ujma.833414.
ISNAD Dragomır, Sever. “Additive Refinements and Reverses of Young’s Operator Inequality Via a Result of Cartwright and Field”. Universal Journal of Mathematics and Applications 4/1 (March 2021), 1-8. https://doi.org/10.32323/ujma.833414.
JAMA Dragomır S. Additive Refinements and Reverses of Young’s Operator Inequality Via a Result of Cartwright and Field. Univ. J. Math. Appl. 2021;4:1–8.
MLA Dragomır, Sever. “Additive Refinements and Reverses of Young’s Operator Inequality Via a Result of Cartwright and Field”. Universal Journal of Mathematics and Applications, vol. 4, no. 1, 2021, pp. 1-8, doi:10.32323/ujma.833414.
Vancouver Dragomır S. Additive Refinements and Reverses of Young’s Operator Inequality Via a Result of Cartwright and Field. Univ. J. Math. Appl. 2021;4(1):1-8.

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