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Optimal bounds for two Seiffert-like means by arithmetic mean and harmonic 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, using the monotone form of L’Hospital’s rule, its extension, and the criterion for the monotonicity of the different sign judgment function of the front and back breaking coefficient signs of the power series of a single function, we establish the exponential inequalities with all nonzero number \(p\in \mathbb {R} \) for two Seiffert-like means, called tangent mean and hyperbolic sine mean, bounded by arithmetic mean \(\textbf{A}\) and harmonic mean \(\textbf{H}\) . Meanwhile we show two double inequalities for these two Seiffert-like means bounded by the weighted geometric mean of \(\textbf{H}\) and \(\textbf{A}\) .

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Gongshang University, Hangzhou, 310018, Zhejiang, China

    Ling Zhu

  2. Faculty of Electrical Engineering, University of Belgrade, Bulevar kralja Aleksandra 73, 11000, Belgrade, Serbia

    Ling Zhu & Branko Malešević

Authors
  1. Ling Zhu
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  2. Branko Malešević
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Correspondence to Ling Zhu.

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Zhu, L., Malešević, B. Optimal bounds for two Seiffert-like means by arithmetic mean and harmonic mean. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 59 (2023). https://doi.org/10.1007/s13398-023-01387-w

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  • DOI: https://doi.org/10.1007/s13398-023-01387-w

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