• A double inequality for bounding Toader mean by the centroidal mean

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/124/04/0527-0531

    • Keywords

       

      Toader mean; centroidal mean; complete elliptic integral; double inequality.

    • Abstract

       

      In this paper, the authors find the best numbers 𝛼 and 𝛽 such that $\overline{C}(\alpha a+ (1 - \alpha)b$, $\alpha b + (1 - \alpha)a) \lt T (a, b) \lt \overline{C} (\beta a + (1 - \beta)b, \beta b + (1 - \beta)a)$ for all 𝑎, $b \gt 0$ with $a \neq b$, where $\overline{C}(a, b) = \frac{2(a^{2}+ab+b^{2})}{3(a+b)}$ and $T(a, b) = \frac{2}{\pi} \int^{\pi/2}_{0}\sqrt{a^{2}\cos^{2}\theta + b^{2}\sin^{2} \theta} {\rm d}\theta$ denote respectively the centroidal mean and Toader mean of two positive numbers 𝑎 and 𝑏.

    • Author Affiliations

       

      Yun Hua1 Feng Qi2

      1. Department of Information Engineering, Weihai Vocational College, Weihai City, Shandong Province 264210, China
      2. College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region 028043, China
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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