Abstract and Applied Analysis

Sharp Power Mean Bounds for Sándor Mean

Yu-Ming Chu, Zhen-Hang Yang, and Li-Min Wu

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We prove that the double inequality Mp(a,b)<X(a,b)<Mq(a,b) holds for all a,b>0 with ab if and only if p1/3 and qlog 2/(1+log 2)=0.4093…, where X(a,b) and Mr(a,b) are the Sándor and rth power means of a and b, respectively.

Article information

Abstr. Appl. Anal., Volume 2015 (2015), Article ID 172867, 5 pages.

First available in Project Euclid: 15 April 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Chu, Yu-Ming; Yang, Zhen-Hang; Wu, Li-Min. Sharp Power Mean Bounds for Sándor Mean. Abstr. Appl. Anal. 2015 (2015), Article ID 172867, 5 pages. doi:10.1155/2015/172867. https://projecteuclid.org/euclid.aaa/1429103741

Export citation


  • P. S. Bullen, D. S. Mitrinovic, and P. M. Vasić, Means and Their Inequalities, D. Reidel, Dordrecht, The Netherlands, 1988.
  • H.-J. Seiffert, “Aufgabe $\beta $16,” Die Wurzel, vol. 29, pp. 221–222, 1995.
  • A. A. Jagers, “Solution of problem 887,” Nieuw Archief voor Wiskunde, vol. 12, no. 4, pp. 230–231, 1994.
  • P. A. Hästö, “A monotonicity property of ratios of symmetric homogeneous means,” Journal of Inequalities in Pure and Applied Mathematics, vol. 3, no. 5, article 71, 23 pages, 2002.
  • P. A. Hästö, “Optimal inequalities between Seiffert's mean and power means,” Mathematical Inequalities & Applications, vol. 7, no. 1, pp. 47–53, 2004.
  • A. Witkowski, “Interpolations of Schwab-Borchardt mean,” Mathematical Inequalities & Applications, vol. 16, no. 1, pp. 193–206, 2013.
  • I. Costin and G. Toader, “Optimal evaluations of some Seiffert-type means by power means,” Applied Mathematics and Computation, vol. 219, no. 9, pp. 4745–4754, 2013.
  • Y.-M. Chu and B.-Y. Long, “Bounds of the Neuman-Sándor mean using power and identric means,” Abstract and Applied Analysis, vol. 2013, Article ID 832591, 6 pages, 2013.
  • H. Alzer, “Ungleichungen für mittelwerte,” Archiv der Mathematik, vol. 47, no. 5, pp. 422–426, 1986.
  • H. Alzer, “Ungleichungen für (e/a)$^{a}$(b/e)$^{b}$,” Elementary Mathematics, vol. 40, pp. 120–123, 1985.
  • F. Burk, “The geometric, logarithmic, and arithmetic mean inequality,” The American Mathematical Monthly, vol. 94, no. 6, pp. 527–528, 1987.
  • T. P. Lin, “The power mean and the logarithmic mean,” The American Mathematical Monthly, vol. 81, pp. 879–883, 1974.
  • A. O. Pittenger, “Inequalities between arithmetic and logarithmic means,” Publikacije Elektrotehničkog Fakulteta. Serija Matematika i Fizika, no. 678–715, pp. 15–18, 1980.
  • A. O. Pittenger, “The symmetric, logarithmic and power means,” Publikacije Elektrotehničkog Fakulteta. Serija Matematika i Fizika, no. 678–715, pp. 19–23, 1980.
  • K. B. Stolarsky, “The power and generalized logarithmic means,” The American Mathematical Monthly, vol. 87, no. 7, pp. 545–548, 1980.
  • H. Alzer and S.-L. Qiu, “Inequalities for means in two variables,” Archiv der Mathematik, vol. 80, no. 2, pp. 201–215, 2003.
  • J. Sándor, “Two sharp inequalities for trigonometric and hyperbolic functions,” Mathematical Inequalities &Applications, vol. 15, no. 2, pp. 409–413, 2012.
  • J. Sándor, “On two new means of two variables,” Notes on Number Theory and Discrete Mathematics, vol. 20, no. 1, pp. 1–9, 2014.
  • J. Sándor, “On certain inequalities for means III,” Archiv der Mathematik, vol. 76, no. 1, pp. 34–40, 2001. \endinput