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Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
Best possible upper and lower bounds are given for the logarithmic and identric mean values in terms of the generalized centroidal mean.
Wydawca
Czasopismo
Rocznik
Tom
Strony
141--152
Opis fizyczny
Bibliogr. 52 poz.
Twórcy
autor
- School of Mathematical Science, Inner Mongolia University, Hohhot 010021, P. R. China
autor
- School of Teacher Education, Huzhou Teachers College, Huzhou 313000, P. R. China
autor
- Department of Mathematics, Huzhou Teachers College, Huzhou 313000, P. R. China
autor
- Department of Mathematics, Huzhou Teachers College, Huzhou 313000, P. R. China
Bibliografia
- [1] H. Alzer, Ungleichungen für (e / a)a(b / e)b, Elem. Math. 40 (1985), 120-123.
- [2] H. Alzer, Ungleichungen für Mittelwerte, Arch. Math. 47 (1986), 422-426.
- [3] H. Alzer and S.-L. Qiu, Inequalities for means in two variables, Arch. Math. 80 (2003), 201-215.
- [4] P. S. Bullen, D. S. Mitrinović and P. M. Vasić, Means and Their Inequalities, D. Reidel Publishing Co., Dordrecht, 1988.
- [5] F. Burk, The geometric, logarithmic, and arithmetic mean inequality, Amer. Math. Monthly 94 (1987), 527-528.
- [6] B. C. Carlson, Algorithms involving arithmetic and geometric means, Amer. Math. Monthly 78 (1971), 496-505.
- [7] B.C. Carlson, The logarithmic mean, Amer. Math. Monthly 79 (1972), 615-618.
- [8] B. C. Carlson and J. L. Gustafson, Total positivity of mean values and hypergeometric functions, SIAM J. Math. Anal. 14 (1983), 389-395.
- [9] Y.-M. Chu and B.-Y. Long, Best possible inequalities between generalized logarithmic mean and classical means, Abstr. Appl. Anal. (2010), article 303286.
- [10] Y.-M. Chu and M.-K. Wang, Optimal inequalities between harmonic, geometric, logarithmic, and arithmetic-geometric means, J. Appl. Math. (2011), article 618929.
- [11] Y.-M. Chu, M.-K. Wang and Z.-K. Wang, A sharp double inequality between harmonic and identric means, Abstr. Appl. Anal. (2011), article 657925.
- [12] Y.-M. Chu, S.-S. Wang and C. Zong, Optimal lower power mean bound for the convex combination of harmonic and logarithmic means, Abstr. Appl. Anal. (2011), article 520648.
- [13] Y.-M. Chu and W.-F. Xia, Inequalities for generalized logarithmic means, J. Inequal. Appl. (2009), article 763252.
- [14] Y.-M. Chu and W.-F. Xia, Two optimal double inequalities between power mean and logarithmic mean, Comput. Math. Appl. 60 (2010), 83-89.
- [15] P. A. Hästö, Optimal inequalities between Seiffert’s mean and power means, Math. Inequal. Appl. 7 (2004), 47-53.
- [16] W Janous, A note on generalized Heronian means, Math. Inequal. Appl. 4 (2011), 369-375.
- [17] P. Kahlig and J. Matkowski, Functional equations involving the logarithmic mean, Z. Angew. Math. Mech. 76 (1996), 385-390.
- [18] E. B. Leach and M. C. Sholander, Extended mean values II, J. Math. Anal. Appl. 92 (1983), 207-223.
- [19] T. P. Lin, The power mean and the logarithmic mean, Amer. Math. Monthly 81 (1974), 879-883.
- [20] H. Liu and X.-J. Meng, The optimal convex combination bounds for the Seiffert’s mean, J. Inequal. Appl. (2011), article 686834.
- [21] B.-Y. Long and Y.-M. Chu, Optimal inequalities for generalized logarithmic, arithmetic, and geometric means, J. Inequal. Appl. (2010), article 806825.
- [22] A. O. Pittenger, Inequalities between arithmetic and logarithmic means, Univ. Beo-grad. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 678-715 (1980), 15-18.
- [23] A. O. Pittenger, The symmetric, logarithmic and power means, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 678-715 (1980), 19-23.
- [24] A. O. Pittenger, The logarithmic mean in n variables, Amer. Math. Monthly 92 (1985), 99-104.
- [25] G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Princeton University Press, Princeton, 1951.
- [26] Y.-F. Qiu, M.-K. Wang and Y.-M. Chu, The optimal generalized Heronian mean bounds for the identric mean, Int. J. Pure Appl. Math. 72 (2011), 19-26.
- [27] Y.-F. Qiu, M.-K. Wang and Y.-M. Chu, The sharp combination bounds of arithmetic and logarithmic means for Seiffert’s mean, Int. J. Pure Appl. Math. 72(2011), 11-18.
- [28] Y-F. Qiu, M.-K. Wang, Y.-M. Chu and G.-D. Wang, Two sharp inequalities for Lehmer mean, identric mean and logarithmci mean, J. Math. Inequal. 5 (2011), 301-306.
- [29] J. Sándor, On the identric and logarithmic means, Aequationes Math. 40 (1990), 261-270.
- [30] J. Sándor, A note on some inequalities for means, Arch. Math. 56 (1991), 471-473.
- [31] J. Sándor, On certain identities for means, Studia Univ. Babes-Bolyai Math. 38 (1993), 7-14.
- [32] J. Sándor, On certain inequalities for means, J. Math. Anal. Appl. 189 (1995), 602-606.
- [33] J. Sándor, On refinements of certain inequalities for means, Arch. Math. 31 (1995), 279-282.
- [34] J. Sándor, Two inequalities for means, Internat. J. Math. Math. Sci. 18 (1995), 621-623.
- [35] J. Sándor, On certain inequalities for means II, J. Math. Anal. Appl. 199 (1996), 629-635.
- [36] J. Sandor, On certain inequalities for means III, Arch. Math. 76 (2001), 34-0.
- [37] J. Sandor and I. Rasa, Inequalities for certain means in two arguments, Nieuw Arch. Wisk (4) 15 (1997), 51-55.
- [38] J. Sandor and T Trif, Some new inequalities for means of two arguments, Int. J. Math. Math. Sci. 25 (2001), 525-532.
- [39] H.-J. Seiffert, Ungleichungen für einen bestimmten Mittelwert, Nieuw. Arch. Wisk. (4)13(1995), 195-198.
- [40] H.-J. Seiffert, Ungleichungen für elementare Mittelwerte, Arch. Math. 64 (1995), 129-131.
- [41] M.-Y Shi, Y.-M. Chu and Y-P. Jiang, Optimal inequalities among various means of two arguments, Abstr. Appl. Anal. (2009), article 694394.
- [42] M.-Y. Shi, Y.-M. Chu and Y.-P. Jiang, Three best inequalities for means in two variables, Int. Math. Forum 5 (2010), 1059-2066.
- [43] M.-Y. Shi, Y.-M. Chu and Y.-P. Jiang, Optimal inequalities related to the power, harmonic and identric mean, Acta Math. Sci. 31A (2011), 1377-1384.
- [44] K. B. Stolarsky, Generalizations of the logarithmic mean, Math. Mag. 48 (1975), 87-92.
- [45] K. B. Stolarsky, The power and generalized logarithmic means, Amer. Math. Monthly 87 (1980), 545-548.
- [46] M. K. Vamanamurthy and M. Vuorinen, Inequalities for means, J. Math. Anal. Appl. 183 (1994), 155-166.
- [47] M.-K. Wang, Y.-M. Chu and Y.-F. Qiu, Some comparison inequalities for generalized Muirhead and identric means, J. Inequal. Appl. (2010), article 295620.
- [48] M.-K. Wang, Z.-K. Wang and Y.-M. Chu, An optimal double inequality between geometric and identric means, Appl. Math. Lett. 25 (2012), 471-475.
- [49] A. Witkowski, Convexity of weighted Stolarsky means, J. Inequal. Pure Appl. Math. 7 (2006), article 73.
- [50] W.-F. Xia and Y.-M. Chu, Optimal inequalities related to the logarithmic, identric, arithmetic and harmonic means, Rev. Anal. Numér. Théor. Approx. 39 (2010), 176-183.
- [51] W.-F. Xia, Y.-M. Chu and G.-D. Wang, The optimal upper and lower power mean bounds for a convex combination of the arithmetic and logarithmic means, Abstr. Appl. Anal. (2010), article 604804.
- [52] C. Zong and Y.-M. Chu, An inequality among identric, geometric and Seiffert’s means, Int. Math. Forum 5 (2010), 1297-1302.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-374ff320-7c29-429d-96ca-86fbeb0f2129