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Nesbitt and Shapiro cyclic sum inequalities for positive definite matrices

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Abstract

The aim of this note is to show that certain number theoretic inequalities, due to Nesbitt and Shapiro, have noncommutative counterparts involving positive definite matrices.

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Acknowledgements

We thank Apoorva Khare for a detailed reading of an earlier draft and for providing valuable comments and feedback. We also thank anonymous referees for their helpful comments. P. N. Choudhury is supported by National Post-Doctoral Fellowship (PDF/2019/000275), from SERB, Government of India. K. C. Sivakumar acknowledges funds received from MATRICS (MTR/2018/001132) of SERB, Government of India.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Science, Bengaluru, 560012, India

    Projesh Nath Choudhury

  2. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600036, India

    K. C. Sivakumar

Authors
  1. Projesh Nath Choudhury
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  2. K. C. Sivakumar
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Correspondence to Projesh Nath Choudhury.

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Communicated by Qingxiang Xu.

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Choudhury, P.N., Sivakumar, K.C. Nesbitt and Shapiro cyclic sum inequalities for positive definite matrices. Adv. Oper. Theory 7, 7 (2022). https://doi.org/10.1007/s43036-021-00171-0

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  • DOI: https://doi.org/10.1007/s43036-021-00171-0

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