Abstract and Applied Analysis
Volume 2010 (2010), Article ID 108920, 12 pages
http://dx.doi.org/10.1155/2010/108920
Research Article
Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means
1Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China
2Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China
Received 29 March 2010; Revised 23 July 2010; Accepted 29 July 2010
Academic Editor: Lance Littlejohn
Copyright © 2010 Yu-Ming Chu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Linked References
- P. S. Bullen, D. S. Mitrinović, and P. M. Vasić, Means and Their Inequalities, vol. 31 of Mathematics and Its Applications, D. Reidel Publishing, Dordrecht, The Netherlands, 1988. View at Zentralblatt MATH · View at MathSciNet
- W.-F. Xia, Y.-M. Chu, and G.-D. Wang, “The optimal upper and lower power mean bounds for a convex combination of the arithmetic and logarithmic means,” Abstract and Applied Analysis, vol. 2010, Article ID 604804, 9 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- M.-Y. Shi, Y.-M Chu, and Y.-P. Jiang, “Optimal inequalities among various means of two arguments,” Abstract and Applied Analysis, Article ID 694394, 10 pages, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- Y.-M Chu and W.-F. Xia, “Two sharp inequalities for power mean, geometric mean, and harmonic mean,” Journal of Inequalities and Applications, Article ID 741923, 6 pages, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- B.-Y. Long and Y.-M Chu, “Optimal power mean bounds for the weighted geometric mean of classical means,” Journal of Inequalities and Applications, Article ID 905679, 6 pages, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- P. A. Hästö, “Optimal inequalities between Seiffert's mean and power means,” Mathematical Inequalities & Applications, vol. 7, no. 1, pp. 47–53, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- H. Alzer and S.-L. Qiu, “Inequalities for means in two variables,” Archiv der Mathematik, vol. 80, no. 2, pp. 201–215, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- F. Burk, “The geometric, logarithmic, and arithmetic mean inequality,” The American Mathematical Monthly, vol. 94, no. 6, pp. 527–528, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
- H. Alzer and W. Janous, “Solution of problem ,” Crux Mathematicorum with Mathematical Mayhem, vol. 13, pp. 173–178, 1987. View at Google Scholar
- H. Alzer, “Ungleichungen für Mittelwerte,” Archiv der Mathematik, vol. 47, no. 5, pp. 422–426, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- H. Alzer, “Ungleichungen für ,” Elemente der Mathematik, vol. 40, pp. 120–123, 1985. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- C. O. Imoru, “The power mean and the logarithmic mean,” International Journal of Mathematics and Mathematical Sciences, vol. 5, no. 2, pp. 337–343, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- A. O. Pittenger, “Inequalities between arithmetic and logarithmic means,” Univerzitet u Beogradu. Publikacije Elektrotehničkog Fakulteta. Serija Matematika i Fizika, no. 678–715, pp. 15–18, 1981. View at Google Scholar
- A. O. Pittenger, “The symmetric, logarithmic and power means,” Univerzitet u Beogradu. Publikacije Elektrotehničkog Fakulteta. Serija Matematika i Fizika, no. 678–715, pp. 19–23, 1981. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- K. B. Stolarsky, “The power and generalized logarithmic means,” The American Mathematical Monthly, vol. 87, no. 7, pp. 545–548, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- T. P. Lin, “The power mean and the logarithmic mean,” The American Mathematical Monthly, vol. 81, pp. 879–883, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- H.-J. Seiffert, “Problem 887,” Nieuw Archief voor Wiskunde, vol. 11, no. 2, pp. 176–176, 1993. View at Google Scholar
- E. Neuman and J. Sándor, “On the Schwab-Borchardt mean,” Mathematica Pannonica, vol. 14, no. 2, pp. 253–266, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- A. A. Jagers, “Solution of problem 887,” Nieuw Archief voor Wiskunde, vol. 12, pp. 230–231, 1994. View at Google Scholar · View at MathSciNet
- H.-J. Seiffert, “Ungleichungen für einen bestimmten Mittelwert,” Nieuw Archief voor Wiskunde. Vierde Serie, vol. 13, no. 2, pp. 195–198, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- J. Sándor, “On certain inequalities for means. III,” Archiv der Mathematik, vol. 76, no. 1, pp. 34–40, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- M.-Y. Shi, Y.-M. Chu, and Y.-P. Jiang, “Three best inequalities for means in two variables,” International Mathematical Forum, vol. 5, no. 22, pp. 1059–1066, 2010. View at Google Scholar