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Norm Inequalities Related to the Heron and Heinz Means

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Abstract

In this article, we present several inequalities treating operator means and the Cauchy–Schwarz inequality. In particular, we present some new comparisons between operator Heron and Heinz means, several generalizations of the difference version of the Heinz means and further refinements of the Cauchy–Schwarz inequality. The techniques used to accomplish these results include convexity and Löwner matrices.

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Authors and Affiliations

  1. Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, 148106, Punjab, India

    Yogesh Kapil & Mandeep Singh

  2. Instituto de Ciencias, Universidad Nacional de General Sarmiento, J. M. Gutierrez 1150, B1613GSX, Los Polvorines, Argentina

    Cristian Conde

  3. Instituto Argentino de Matemática “Alberto P. Calderón”, Saavedra 15 3 piso, C1083ACA, Buenos Aires, Argentina

    Cristian Conde

  4. Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, P. O. Box 1159 , Mashhad, 91775, Iran

    Mohammad Sal Moslehian

  5. Department of Mathematics, University of Sharjah, Sharjah, UAE

    Mohammad Sababheh

  6. Department of Basic Sciences, Princess Sumaya University for Technology, Amman, 11941, Jordan

    Mohammad Sababheh

Authors
  1. Yogesh Kapil
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  2. Cristian Conde
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  3. Mohammad Sal Moslehian
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  4. Mandeep Singh
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  5. Mohammad Sababheh
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Correspondence to Mohammad Sal Moslehian.

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Kapil, Y., Conde, C., Moslehian, M.S. et al. Norm Inequalities Related to the Heron and Heinz Means. Mediterr. J. Math. 14, 213 (2017). https://doi.org/10.1007/s00009-017-1015-6

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  • DOI: https://doi.org/10.1007/s00009-017-1015-6

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