[1]
|
E. F. Beckenbach and R. Bellman, “Inequality,” 4th Edi tion, Springer-Verlag, Berlin, 1984.
|
[2]
|
E. F. Beckenbach and W. Waler, “General Inequalities III,” Birkhauser Verlag, Basel, 1983.
|
[3]
|
P. S. Bullen, “Handbook of Means and Their Inequali ties,” Kluwer Academic Publishers, Dordrecht, 2003.
doi:10.1007/978-94-017-0399-4
|
[4]
|
P. S. Bullen, D. S. Mitrinovic and P. M. Vasic, “Means and Their Inequalities,” D. Reidel Publishing Company, Dordrecht, 1952.
|
[5]
|
P. S. Bullen, “A Chapter on Inequalities,” Southeast Asian Bulletin of Mathematics, Vol. 3, 1979, pp. 8-26.
|
[6]
|
M. J. Cloud and B. C. Drachman, “Inequalities with Ap plications to Engineering,” Springer Verlag, New York, 1998.
|
[7]
|
C. Georgakis, “On the Inequality for the Arithmetic and Geometric Means,” Mathematical Inequalities and Ap plications, Vol. 5, 2002, pp. 215-218.
|
[8]
|
G. Hardy, J. E. Littlewood and G. Pólya, “Inequalities,” 2nd Edition, Cambridge University Press, Cambridge, 1952.
|
[9]
|
Z. Hao, “Note on the Inequality of the Arithmetric and Geometric Means,” Pacific Journal of Mathematics, Vol. 143, No. 1, 1990, pp. 43-46.
|
[10]
|
J. Howard and J. Howard, “Equivalent Inequalities,” The College Mathematics Journal, Vol. 19, No. 4, 1988, pp. 350-354.
|
[11]
|
K. Hu, “Some Problems of Analytic Inequalities (in Chi nese),” Wuhan University Press, Wuhan, 2003.
|
[12]
|
C. A. Infantozzi, “An Introduction to Relations among Inequalities,” Notices of the American Mathematical Society, Vol. 141, 1972, pp. A918-A820.
|
[13]
|
S. Isumino and M. Tominaga, “Estimation in Holder’s Type Inequality,” Mathematical Inequalities and Appli cations, Vol. 4, 2001, pp. 163-187.
|
[14]
|
J. Kuang, “Applied Inequalities (in Chinese),” 3rd Edition, Shandong Science and Technology Press, Shandong, 2004.
|
[15]
|
Y.-C. Li and S. Y. Shaw, “A Proof of Holder’s Inequality Using the Cauchy-Schwarz Inequality,” Journal of Ine qualities in Pure and Applied Mathematics, Vol. 7, No. 2, 2006.
|
[16]
|
C. K. Lin, “Convex Functions, Jensen’s Inequality and Legendre Transformation (in Chinese),” Mathmedia, Academic Sinica, Vol. 19, 1995, pp. 51-57.
|
[17]
|
C. K. Lin, “The Essence and Significance of Cauchy Schwarz’s Inequality (in Chinese),” Mathmedia, Aca demic Sinica, Vol. 24, 2000, pp. 26-42.
|
[18]
|
L. Maligranda, “Why Holder’s Inequality Should Be Called Rogers’ Inequality,” Mathematical Inequalities and Applications, Vol. 1, 1998, pp. 69-83.
|
[19]
|
A. W. Marshall and I. Olkin, “Inequalities: Theory of Majorization and Its Applications,” Academic Press, New York, 1979.
|
[20]
|
D. S. Mitrinovic, “Analytic Inequalities,” Springer-Verlag, Berlin, 1970.
|
[21]
|
D. S. Mitrinovic, J. E. Pecaric and A. M. Fink, “Classical and New Inequalities in Analysis,” Klumer Academic Publisher, Dordrecht, 1993.
doi:10.1007/978-94-017-1043-5
|
[22]
|
D. S. Mitrinovic and J. E. Pevaric, “Bernoulli’s Inequa lity,” Rendiconti del Circolo Matematico di Palermo, Vol. 42, No. 3, 1993, pp. 317-337.
|
[23]
|
D. J. Newman, “Arithmetric, Geometric Inequality,” The American Mathematical Monthly, Vol. 67, No. 9, 1960, p. 886. doi:10.2307/2309460
|
[24]
|
N. O. Ozeki and M. K. Aoyaki, “Inequalities (in Japa nese),” 3rd Edition, Maki Shoten, Tokyo, 1967.
|
[25]
|
J. E. Pecaric, “On Bernoulli’s Inequality,” Akad. Nauk. Umjet. Bosn. Hercegov. Rad. Odelj. Prirod. Mat. Nauk, Vol. 22, 1983, pp. 61-65.
|
[26]
|
J. Pecaric and K. B. Stolarsky, “Carleman’s Inequality: History and New Generalizations,” Aequationes Mathe maticae, Vol. 61, No. 1-2, 2001, pp. 49-62.
doi:10.1007/s000100050160
|
[27]
|
J. Pecaric and S. Varacance, “A New Proof of the Arith metic Mean—The Geometric Mean Inequality,” Journal of Mathematical Analysis and Applications, Vol. 215, No. 2, 1997, pp. 577-578.doi:10.1006/jmaa.1997.5616
|
[28]
|
J. Rooin, “Some New Proofs for the AGM Inequality,” Mathematical Inequalities and Applications, Vol. 7, No. 4, 2004, pp. 517-521.
|
[29]
|
N. Schaumberger, “A Coordinate Approach to the AM GM Inequality,” Mathematics Magazine, Vol. 64, No. 4, 1991, p. 273. doi:10.2307/2690837
|
[30]
|
S.-C. Shyy, “Convexity,” Dalian University of Technolgy Press, Dalian, 2011.
|
[31]
|
X. H. Sun, “On the Generalized Holder Inequalities,” Soochow Journal of Mathematics, Vol. 23, 1997, pp. 241 252.
|
[32]
|
C. L. Wang, “Inequalities of the Rado-Popoviciu Type for Functions and Their Applications,” Journal of Mathe matical Analysis and Applications, Vol. 100, No. 2, 1984, pp. 436-446. doi:10.1016/0022-247X(84)90092-1
|
[33]
|
X. T. Wang, H. M. Su and F. H. Wang, “Inequalities, Theory, Methods (in Chinese),” Henan Education Publi cation, Zhengzhou, 1967.
|
[34]
|
J. Wen, W. Wang, H. Zhou and Z. Yang, “A Class of Cylic Inequalities of Janous Type (in Chinese),” Journal of Chengdu University, Vol. 22, 2003, pp. 25-29.
|
[35]
|
C. X. Xue, “Isolation and Extension of Bernoulli Ine qualities (in Chinese),” Journal of Gansu Education Col lege, Vol. 13, No. 3, 1999, pp. 5-7.
|