1 |
Zh.-H. Yang, Some identities for means and applications, RGMIA Res. Rep. Coll. 8 (2005), no. 3, Art. 17.
|
2 |
Zh.-H. Yang, On the homogeneous functions with two parameters and its monotonicity, J. Inequal. Pure Appl. Math. 6 (2005), no. 4, Article 101, 11 pp.
|
3 |
Zh.-H. Yang, On the log-convexity of two-parameter homogeneous functions, Math. Inequal. Appl. 10 (2007), no. 3, 499-516.
|
4 |
Zh.-H. Yang, On the monotonicity and log-convexity of a four-parameter homogeneous mean, J. Ine. Appl. 2008 (2008), Art. ID 149286, 12 pages, doi:10.1155/2008/149286.
DOI
ScienceOn
|
5 |
E. B. Leach and M. Sholander, Extended mean values II, J. Math. Anal. Appl. 92 (1983), no. 1, 207-223.
DOI
|
6 |
T. P. Lin, The power mean and the logarithmic mean, Amer. Math. Monthly 81 (1974), 879-883.
DOI
ScienceOn
|
7 |
E. Neuman and J. Sandor, On certain means of two arguments and their extensions, Int. J. Math. Math. Sci. 2003 (2003), no. 16, 981-993.
DOI
ScienceOn
|
8 |
E. Neuman and J. Sandor, Inequalities involving Stolarsky and Gini means, Math. Pannon. 14 (2003), no. 1, 29-44.
|
9 |
E. Neuman, A generalization of an inequality of Jia and Cau, J. Inequal. Pure Appl. Math. 5 (2004), no. 1, Article 15, 4 pp.
|
10 |
B. Ostle and H. L. Terwilliger, A comparison of two means, Proc. Montana Acad. Sci. 17 (1957), 69-70.
|
11 |
Zs. Pales, Inequalities for sums of powers, J. Math. Anal. Appl. 131 (1988), no. 1, 265-270.
DOI
|
12 |
Zs. Pales, Inequalities for differences of powers, J. Math. Anal. Appl. 131 (1988), no. 1, 271-281.
DOI
|
13 |
A. O. Pittenger, Inequalities between arithmetic and logarithmic means, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 678-715 (1980), 15-18.
|
14 |
F. Qi, Logarithmic convexity of extended mean values, Proc. Amer. Math. Soc. 130 (2002), no. 6, 1787-1796.
DOI
ScienceOn
|
15 |
F. Qi, On a two-parameter family of nonhomogeneous mean values, Tamkang J. Math. 29 (1998), no. 2, 155-163.
|
16 |
J. Sandor, On the identric and logarithmic means, Aequationes Math. 40 (1990), no. 2-3, 261-270.
DOI
|
17 |
J. Sandor, On certain identities for means, Studia Univ. Babes-Bolyai, Math. 37 (1993), no. 4, 7-14.
|
18 |
J. Sandor, On refinements of certain inequalities for means, Arch. Math. (Brno) 31 (1995), no. 4, 279-282.
|
19 |
H. Alzer, Uer eine einparametrige familie von Mitlewerten, Bayer. Akad. Wiss. Math.-Natur. Kl. Sitzungsber 1987 (1988), 23-29.
|
20 |
H. Alzer, Uer eine einparametrige familie von Mitlewerten. II, Bayer. Akad. Wiss. Math.-Natur. Kl. Sitzungsber 1988 (1989), 23-29.
|
21 |
H. Alzer, On Stolarsky's mean value family, Int. J. Math. Educ. Sci. Technol. 20 (1989), no. 1, 186-189.
|
22 |
J. L. Brenner, A unified treatment and extension of some means of classical analysis I. Comparison theorems, J. Combin. Inform. System Sci. 3 (1978), no. 4, 175-199.
|
23 |
F. Burk, By all means, Amer. Math. Monthly 92 (1985), no. 1, 50.
DOI
|
24 |
B. C. Carlson, Some inequalities for hypergeometric functions, Proc. Amer. Math. Soc. 17 (1966), 32-39.
DOI
ScienceOn
|
25 |
B. C. Carlson, The logarithmic mean, Amer. Math. Monthly 79 (1972), 615-618.
DOI
ScienceOn
|
26 |
W.-S. Cheung and F. Qi, Logarithmic convexity of the one-parameter mean values, Taiwanese J. Math. 11 (2007), no. 1, 231-237.
DOI
|
27 |
E. L. Dodd, Some generalizations of the logarithmic mean and of similar means of two variates which become indeterminate when the two variates are equal, Ann. Math. Stat. 12 (1941), 422-428.
DOI
ScienceOn
|
28 |
C. Gini, Diuna formula comprensiva delle media, Metron 13 (1938), 3-22.
|
29 |
P. A. Hasto, A monotonicity property of ratios of symmetric homogeneous means, J. Inequal. Pure Appl. Math. 3 (2002), no. 5, Article 71, 23 pp.
|
30 |
G. Jia and J.-D. Cao, A new upper bound of the logarithmic mean, J. Inequal. Pure Appl. Math. 4 (2003), no. 4, Article 80, 4 pp.
|
31 |
O. Kouba, New bounds for the identric mean of two arguments, J. Inequal. Pure Appl. Math. 9 (2008), no. 3, Article 71, 6 pp.
|
32 |
E. B. Leach and M. Sholander, Extended mean values, Amer. Math. Monthly 85 (1978), no. 2, 84-90.
DOI
ScienceOn
|
33 |
H. Alzer, Ungleichungen fur Mittelwerte, Arch. Math. 47 (1986), no. 5, 422-426.
DOI
ScienceOn
|
34 |
H. Alzer, Two inequalities for means, C. R. Math. Rep. Acad. Sci. Canada 9 (1987), no.1, 11-16.
|
35 |
H. Alzer, Aufgabe 987, Elem. Math. 43 (1988), 93.
|
36 |
J. Sandor and T. Trif, Some new inequalities for means of two arguments, Int. J. Math. Math. Sci. 25 (2001), no. 8, 525-532.
DOI
|
37 |
K. B. Stolarsky, Generalizations of the logarithmic mean, Math. Mag. 48 (1975), 87-92.
DOI
ScienceOn
|
38 |
K. B. Stolarsky, The power and generalized logarithmic means, Amer. Math. Monthly 87 (1980), no. 7, 545-548.
DOI
ScienceOn
|
39 |
T. Trif, Note on certain inequalities for means in two variables, J. Inequal. Pure Appl. Math. 6 (2005), no. 2, Article 43, 5 pp.
|
40 |
R. Yang and D. Cao, Generalizations of the logarithmic mean, J. Ningbo Univ. 2 (1989), no. 1, 105-108.
|
41 |
Zh.-H. Yang, Simple discriminances of convexity of homogeneous functions and applications, Gaodeng Shuxue Yanjiu (Study in College Mathematics) 4 (2004), no. 7, 14-19.
|
42 |
Zh.-H. Yang, On the monotonicity and log-convexity for one-parameter homogeneous functions, RGMIA Res. Rep. Coll. 8 (2005), no. 2, Art. 14.
|