[1]  Gini C. Di una formula compresive delle medie. Metron, 1938, 13: 3--22
 
[2]  Pá}les Z. Inequalities for differences of powers. J Math Anal Appl, 1988, 131(1): 271--281

[3]  Leach E B, Sholander M C. Extended mean values. Amer Math Monthly, 1978, 85(2): 84--90

[4]  Neuman E, Sándor J. Inequalities involving Stolarsky and Gini means. Math Pannonica, 2003, 14(1): 29--44

[5]  Stolarsky K B. Generalizations of the logarithmic mean. Math Mag, 1975, 48(2): 87--92

[6]  Rassias Th M. Survey on Classical Inequalities. Dordrecht: Kluwer Acad Publ, 2000

[7]  Marshall A W, Olkin I. Inequalities: Theory of Majorization and Its Applications. New York: Academic Press, 1979

[8]  Greene R E, Wu H. C^∞  convex functions and manifolds of positive curvature. Acta Math, 1976, 137(3/4):
209--245

[9]  Greene R E, Shiohama K. Convex functions on complete noncompact manifolds: topological structure. Invent Math, 1981, 63(1): 129--157

[10]  Aujla J S, Silva F C. Weak majorization inequalities and convex functions. Linear Algebra Appl, 2003, 369: 217--233

[11]  Lu G Z, Manfredi J J, Stroffolini B. Convex functions on the Heisenberg group. Calc Var Partial Differential Equations, 2004, 19(1): 1--22

[12]  Hwang F K, Rothblum U G. Partition-optimization with Schur sum objective functions. SIAM J Discrete Math, 2004/2005, 18(3): 512--524

[13]  Zhang X M, Schur-convex functions and isoperimetric inequalities. Proc Amer Math Soc, 1998, 126(2): 461--470

[14]  Stepniak C. Stochastic ordering and Schur-convex functions in comparison of linear experiments. Metrika, 1989, 36(5): 291--298

[15]  Constantine G M. Schur-convex functions on the spetra of graphs. Discrete Math, 1983, 45(2/3): 181--188

[16]  Titarenko V, Yagola A. Linear ill-posed problems on sets of convex functions on two-dimensional sets. J Inverse Ill-Posed Probl, 2006, 14(7): 735--750

[17]  Ruan Y B, Chen S X. Approximation of convex functions on the dual spaces. Acta Math Sci, 2004, 24A(1): 116--122 (In Chinese)

[18]  Garofalo N, Tournier F. New properties of convex functions in the Heisenberg group. Trans Amer Math Soc, 2006, 358(5): 2011--2055

[19]  Schn\"{u}rer O C. Convex functions with unbounded gradient. Results Math, 2005, 48(1/2): 158--161

[20]  Singh T. Degree of approximation by harmonic means of Fourier-Laguerre expansions. Publ Math Debrecen, 1977, 24(1/2): 53--57

[21] Foster D M E, Phillips G M. The arithmetic-harmonic mean. Math Comp, 1984, 42(165): 183--191

[22] Firey W J. Mean cross-section measures of harmonic means of convex bodies. Pacific J Math, 1961, 11: 1263--1266

[23]  Aldous D. The harmonic mean formula for probabilities of unions: applications to sparse random graphs. Discrete Math, 1989, 76(3): 167--176

[24]  Webster R J. The harmonic means of diagonals of doubly-stochastic matrices. Linear and Multilinear Algebra, 1983, 13(4): 367--369

[25] Komarova N L, Rivin I. Harmonic mean, random polynomials and stochastic matrices. Adv  Appl Math, 2003, 31(2): 501--526

[26]  Alzer H. On Gautschi's harmonic mean inequality for the gamma function. J Comput Appl Math, 2003, 157(1): 243--249

[27]  Alzer H. A harmonic mean inequality for the gamma function. J Comput Appl Math, 1997, 87(2): 195--198

[28]  Gautschi W. A harmonic mean inequality for the gamma function. SIAM J Math Anal, 1974, 5: 278--281

[29]  Mercer P R. Refined arithmetic, geomtric and harmonic mean inequalities. Rocky Mountain J Math, 2003, 33(4): 1459--1464

[30]  Sagae M, Tanabe K. Upper and lower bounds for the arithmetic-geometric-harmonic means of positive definite matrices. Linear and Multilinear Algebra, 1994, 37(4): 279--282

[31]  Alzer H. An inequality for arithmetic and harmonic means. Aequationes Math, 1993, 46(3): 257--263

[32]  Mathias R. An arithmetic-geometric-harmonic mean inequality involving Hadamard products. Linear Algebra Appl, 1993, 184: 71--78

[33]  Liu W. A strong limit theorem for the harmonic mean of the random transition probabilities of finite nonhomogeneous Markov chains. Acta Math Sci, 2000, 20(1): 81--84 (In Chinese)

[34]  Aczél J. A generalization of the notion of convex functions. Norske Vid Selsk Forh, 1947, 19(24): 87--90

[35]  Vamanamurthy M K, Vuorinen M. Inequalities for means. J Math Anal Appl, 1994, 183(1): 155--166

[36] Roberts A W, Varberg D E. Convex Functions. New York: Academic Press, 1973

[37]  Niculescu C P, Persson L E. Convex Functions and Their Applications. New York: Springer-Verlag, 2006

[38] Matkowski J. Convex functions with respect to a mean and a characterization of quasi-arithmetic means. Real Anal Exchange, 2003/2004, 29(1): 229--246

[39]  Bullen P S, Mitrinovi\'{c} D S, Vasi\'{c} P M. Means and Their Inequalities. Dordrecht: Reidel, 1988

[40]  Das C, Mishra S, Pradhan P K. On harmonic convexity (concavity) and application to non-linear programming problems. Opsearch, 2003, 40(1): 42--51

[41]  Das C, Roy K L, Jena K N. Harmonic convexity and application to optimization problems. Math Ed, 2003, 37(2): 58--64

[42] Kar K, Nanda S. Harmonic convexity of composite functions. Proc Nat Acad Sci India Sect A, 1992, 62(1): 77--81

[43] Anderson G D, Vamanamurthy M K, Vuorinen M. Generalized convexity and inequalities. J Math Anal Appl, 2007, 335(2): 1294--1308

[44]  Stolarsky K B. The power and generalized logarithmic means. Amer Math Monthly, 1980, 87(7): 545--548

[45]  Qi F. A note on Schur-convexity of extended mean values. Rocky Mountain J Math, 2005, 35(5): 1787--1793

[46]  Qi F, Sándor J, Dragomir S S, Sofo A. Notes on the Schur-convexity of the extended mean values. Taiwanese J Math, 2005, 9(3): 411--420

[47]  Shi H N, Wu Sh H, Qi F. An alternative note on the Schur-convexity of the extended mean values. Math Inequal Appl, 2006, 9(2): 219--224

[48]  Chu Y M, Zhang X M. Necessary and sufficient conditins such that extended mean values are Schur-convex or Schur-concave. J Math Kyoto Univ, 2008, 48(1): 229--238

[49] Sándor J. The Schur-convexity of Stolarsky and Gini means. Banach J Math Anal, 2007, 1(2): 212--215