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New bounds for a generalized logarithmic mean and Heinz mean

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this paper, by using the monotone form of L’Hospital’s rule and a criterion for the monotonicity of quotient of two power series we present some sharp bounds for a generalized logarithmic mean and Heinz mean by weighted means of harmonic mean, geometric mean, arithmetic mean, two power means \(M_{1/2}(a,b)\) and \(M_{2}(a,b)\). Operator versions of these inequalities are obtained except for those related to the quadratic mean \( M_{2}(a,b)\).

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Acknowledgements

The authors are thankful to reviewers for reviewers’ careful corrections and valuable comments on the original version of this paper.

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  1. Hangzhou College of Commerce, Zhejiang Gongshang University, Hangzhou, China

    Jiahua Ding

  2. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, China

    Ling Zhu

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  1. Jiahua Ding
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Ding, J., Zhu, L. New bounds for a generalized logarithmic mean and Heinz mean. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 67 (2024). https://doi.org/10.1007/s13398-024-01566-3

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