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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 832591, 6 pages
http://dx.doi.org/10.1155/2013/832591
Research Article
Bounds of the Neuman-Sándor Mean Using Power and Identric Means
1Department of Mathematics, Huzhou Teachers College, Huzhou, Zhejiang 313000, China
2School of Mathematics Science, Anhui University, Hefei, Anhui 230039, China
Received 8 November 2012; Revised 4 January 2013; Accepted 11 January 2013
Academic Editor: Wenchang Sun
Copyright © 2013 Yu-Ming Chu and Bo-Yong Long. 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
- E. Neuman and J. Sándor, “On the Schwab-Borchardt mean,” Mathematica Pannonica, vol. 14, no. 2, pp. 253–266, 2003. View at Zentralblatt MATH · View at MathSciNet
- 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 MathSciNet
- J. Sándor, “On the identric and logarithmic means,” Aequationes Mathematicae, vol. 40, no. 2-3, pp. 261–270, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- J. E. Pečarić, “Generalization of the power means and their inequalities,” Journal of Mathematical Analysis and Applications, vol. 161, no. 2, pp. 395–404, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- J. Sándor, “A note on some inequalities for means,” Archiv der Mathematik, vol. 56, no. 5, pp. 471–473, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- J. Sándor and I. Raşa, “Inequalities for certain means in two arguments,” Nieuw Archief voor Wiskunde, vol. 15, no. 1-2, pp. 51–55, 1997. View at Zentralblatt MATH · View at MathSciNet
- J. Sándor and T. Trif, “Some new inequalities for means of two arguments,” International Journal of Mathematics and Mathematical Sciences, vol. 25, no. 8, pp. 525–532, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- T. Trif, “On certain inequalities involving the identric mean in variables,” Universitatis Babeş-Bolyai, vol. 46, no. 4, pp. 105–114, 2001. 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
- 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 Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- S. Wu, “Generalization and sharpness of the power means inequality and their applications,” Journal of Mathematical Analysis and Applications, vol. 312, no. 2, pp. 637–652, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- O. Kouba, “New bounds for the identric mean of two arguments,” Journal of Inequalities in Pure and Applied Mathematics, vol. 9, no. 3, article 71, 6 pages, 2008. View at Zentralblatt MATH · View at MathSciNet
- L. Zhu, “New inequalities for means in two variables,” Mathematical Inequalities & Applications, vol. 11, no. 2, pp. 229–235, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- L. Zhu, “Some new inequalities for means in two variables,” Mathematical Inequalities & Applications, vol. 11, no. 3, pp. 443–448, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- E. Neuman and J. Sándor, “Companion inequalities for certain bivariate means,” Applicable Analysis and Discrete Mathematics, vol. 3, no. 1, pp. 46–51, 2009. View at Publisher · 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, vol. 2009, Article ID 741923, 6 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- Y.-M. Chu, Y.-F. Qiu, and M.-K. Wang, “Sharp power mean bounds for the combination of Seiffert and geometric means,” Abstract and Applied Analysis, vol. 2010, Article ID 108920, 12 pages, 2010. View at Publisher · 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, vol. 2010, Article ID 905679, 6 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- M.-K. Wang, Y.-M. Chu, and Y.-F. Qiu, “Some comparison inequalities for generalized Muirhead and identric means,” Journal of Inequalities and Applications, vol. 2010, Article ID 295620, 10 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- S. Gao, “Inequalities for the Seiffert's means in terms of the identric mean,” Journal of Mathematical Sciences, vol. 10, no. 1-2, pp. 23–31, 2011. View at MathSciNet
- Y.-M. Chu, M.-K. Wang, and Z.-K. Wang, “A sharp double inequalities between harmonic and identric means,” Abstract and Applied Analysis, vol. 2011, Article ID 657935, 7 pages, 2011. View at Publisher · View at Google Scholar
- Y.-F. Qiu, M.-K. Wang, Y.-M. Chu, and G.-D. Wang, “Two sharp inequalities for Lehmer mean, identric mean and logarithmic mean,” Journal of Mathematical Inequalities, vol. 5, no. 3, pp. 301–306, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- M.-K. Wang, Z.-K. Wang, and Y.-M. Chu, “An optimal double inequality between geometric and identric means,” Applied Mathematics Letters, vol. 25, no. 3, pp. 471–475, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- Y. M. Li, B. Y. Long, and Y. M. Chu, “Sharp bounds for the Neuman-Sándor mean in terms of generalized logarithmic mean,” Journal of Mathematical Inequalities, vol. 6, no. 4, pp. 567–577, 2012.
- E. Neuman, “A note on a certain bivariate mean,” Journal of Mathematical Inequalities, vol. 6, no. 4, pp. 637–643, 2012.
- T. H. Zhao, Y. M. Chu, and B. Y. Liu, “Optimal bounds for Neuman-Sándor mean in terms of the convex combinations of harmonic, geometric, quadratic, and contraharmonic means,” Abstract and Applied Analysis, vol. 2012, Article ID 302635, 9 pages, 2012. View at Publisher · View at Google Scholar
- K. Baumgartner, “Zur Unauflösbarkeit für ,” Elemente der Mathematik, vol. 40, no. 5, p. 123, 1985. View at Zentralblatt MATH · View at MathSciNet
- 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
- F. Burk, “Notes: 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
- 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
- A. O. Pittenger, “Inequalities between arithmetic and logarithmic means,” Univerzitet u Beogradu, no. 678–715, pp. 15–18, 1980. View at Zentralblatt MATH · View at MathSciNet
- A. O. Pittenger, “The symmetric, logarithmic and power means,” Univerzitet u Beogradu, no. 678–715, pp. 19–23, 1980. View at Zentralblatt MATH · View at MathSciNet
- A. A. Jagers, “Solution of problem 887,” Nieuw Archief voor Wiskunde, vol. 12, pp. 230–231, 1994.
- J. Sándor, “On certain identities for means,” Universitatis Babeş-Bolyai, vol. 38, no. 4, pp. 7–14, 1993. View at Zentralblatt MATH · View at MathSciNet