- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 830585, 11 pages
Inequalities between Arithmetic-Geometric, Gini, and Toader Means
Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China
Received 24 August 2011; Accepted 20 October 2011
Academic Editor: Muhammad Aslam Noor
Copyright © 2012 Yu-Ming Chu and Miao-Kun Wang. 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.
- I. Raşa and M. Ivan, “Some inequalities for means II,” in Proceedings of the Itinerant Seminar on Functional Equations, Approximation and Convexity, pp. 75–79, Cluj-Napoca, Romania, May 2001.
- J. Sándor, “A note on the Gini means,” General Mathematics, vol. 12, no. 4, pp. 17–21, 2004.
- 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.
- P. S. Bullen, D. S. Mitrinović, and P. M. Vasić, Means and their Inequalities, vol. 31, D. Reidel Publishing, Dordrecht, The Netherlands, 1988.
- P. A. Hästö, “Optimal inequalities between Seiffert's mean and power means,” Mathematical Inequalities & Applications, vol. 7, no. 1, pp. 47–53, 2004.
- H. Alzer and S.-L. Qiu, “Inequalities for means in two variables,” Archiv der Mathematik, vol. 80, no. 2, pp. 201–215, 2003.
- K. C. Richards, “Sharp power mean bounds for the Gaussian hypergeometric function,” Journal of Mathematical Analysis and Applications, vol. 308, no. 1, pp. 303–313, 2005.
- Gh. Toader, “Some mean values related to the arithmetic-geometric mean,” Journal of Mathematical Analysis and Applications, vol. 218, no. 2, pp. 358–368, 1998.
- G. D. Anderson, M. K. Vamanamurthy, and M. K. Vuorinen, Conformal Invariants, Inequalities, and Quasiconformal Maps, John Wiley & Sons, New York, NY, USA, 1997.
- M. Vuorinen, “Hypergeometric functions in geometric function theory,” in Special Functions and Differential Equations (Madras, 1997), pp. 119–126, Allied, New Delhi, India, 1998.
- S.-L. Qiu and J.-M. Shen, “On two problems concerning means,” Journal of Hangzhou Insitute of Electronic Engineering, vol. 17, no. 3, pp. 1–7, 1997 (Chinese).
- R. W. Barnard, K. Pearce, and K. C. Richards, “An inequality involving the generalized hypergeometric function and the arc length of an ellipse,” SIAM Journal on Mathematical Analysis, vol. 31, no. 3, pp. 693–699, 2000.
- H. Alzer and S.-L. Qiu, “Monotonicity theorems and inequalities for the complete elliptic integrals,” Journal of Computational and Applied Mathematics, vol. 172, no. 2, pp. 289–312, 2004.
- B. C. Carlson and M. Vuorinen, “Inequality of the AGM and the logarithmic mean,” SIAM Review, vol. 33, no. 4, p. 655, 1991.
- M. K. Vamanamurthy and M. Vuorinen, “Inequalities for means,” Journal of Mathematical Analysis and Applications, vol. 183, no. 1, pp. 155–166, 1994.
- P. Bracken, “An arithmetic-geometric mean inequality,” Expositiones Mathematicae, vol. 19, no. 3, pp. 273–279, 2001.
- F. Qi and A. Sofo, “An alternative and united proof of a double inequality for bounding the arithmetic-geometric mean,” University Politehnica of Bucharest Scientific Bulletin Series A, vol. 71, no. 3, pp. 69–76, 2009.
- Y.-M. Chu and M.-K. Wang, “Optimal Lehmer mean bounds for the Toader mean,” Results in Mathematics. In press.
- B.-N. Guo and F. Qi, “Some bounds for the complete elliptic integrals of the first and second kinds,” Mathematical Inequalities & Applications, vol. 14, no. 2, pp. 323–334, 2011.