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THE STOLARSKY TYPE FUNCTIONS AND THEIR MONOTONICITIES

Yıl 2009, Cilt: 38 Sayı: 2, 119 - 128, 01.02.2009

Öz

In this paper, we give the definition of a Stolarsky type function, and obtain its monotonicity. By using these results, we establish a series of means and their monotonicities in n variables.

Kaynakça

  • Hardy, G. H., Littlewood, J. E. and Polya, G. Inequalities (2nd.ed., Cambridge University Press, Cambrige, 1959).
  • Kuang, J. -C. Applied Inequalities (Hunan Education Press, 2nd. Ed., 1993), 39–49. (in Chinese).
  • Leach, E. B. and Sholander, M. C. Extended mean values, Amer. Math. Monthly 85, 84–90, 1978.
  • Leach, E. B. and Sholander, M. C. Extended mean values, J. Math. Anal. Appl. 92, 207–223, 1983.
  • Lokesha, V. and Zhang, Z. -H. The weighted Heron dual mean in n variables, Adv. Stud. Contemp. Math. (Kyungshang) 13 (2), 165–170, 2006.
  • Pe˘cari´c, J. and ˘Simi´c, V. Stolarsky-Tobey mean in n variables, Math. Inequal. Appl. 2 (3), 328–341, 1999. [7] Qi, F. Generalized weighted mean values with two parameters, Proc. Royal Soc. London, Series, Math. Physical Engineering Sci. 454, 2723–2732, 1998.
  • Qi, F. On a two-parameter family of nonhomogeneous mean values, Tamkang J. Math. 29, 155–163, 1998. [9] Stolarsky, K. B. Generalizations of the logarithmic mean, Math. Mag. 48, 87–92, 1975.
  • Xiao, Z. -G. and Zhang, Z. -H. The Henleman mean of n positive numbers, J. Yueyang Normal Univ. 14 (2), 1–5, 2001 (in Chinese).
  • Xiao, Z. -G. and Zhang, Z. -H. The Stolarsky mean of n positive numbers, J. Yueyang Normal Uinv. 14 (4), 5–8, 2001 (in Chinese).
  • Xiao, Z. -G., Zhang, Z. -H., Lokesha, V. and Nagaraja, K. M. A class of new three-parameter generalized weighted means, Int. J. Appl. Math. Stat. 11 (7), 193–202, 2007.
  • Xiao, Z. -G, Zhang, Z. -H., Lokesha, V. and Tang, R. The two-parameter mean of n variables, Int. Rev. Pure Appl. Math. 1 (1), 93–111, 2005.
  • Xiao, Z. -G., Zhang, Z. -H. and Qi, F. A type of mean values of several positive numbers with two parameters, Nonlinear Funct. Anal. Appl. 12, 687–702, 2007.
  • Zhang, Z. -H. Three classes of new means in n+1 variables and their applications, J. Hunan Ed. Inst. 15 (5), 130–136, 1997 (in Chinese).
  • Zhang, Z. -H., Lokesha, V. and Xiao, Z. -G. The weighted Heron mean in n variables, J. Anal. Comput. 1 (1), 57–68, 2005.
  • Zhang, Z. -H., Xiao, Z. -G. and Srivastava, H. M. A general family of weighted elementary symmetric means, Appl. Math. Lett. (2008), doi:10.1016/j.aml.2007.12.030

THE STOLARSKY TYPE FUNCTIONS AND THEIR MONOTONICITIES

Yıl 2009, Cilt: 38 Sayı: 2, 119 - 128, 01.02.2009

Öz

Kaynakça

  • Hardy, G. H., Littlewood, J. E. and Polya, G. Inequalities (2nd.ed., Cambridge University Press, Cambrige, 1959).
  • Kuang, J. -C. Applied Inequalities (Hunan Education Press, 2nd. Ed., 1993), 39–49. (in Chinese).
  • Leach, E. B. and Sholander, M. C. Extended mean values, Amer. Math. Monthly 85, 84–90, 1978.
  • Leach, E. B. and Sholander, M. C. Extended mean values, J. Math. Anal. Appl. 92, 207–223, 1983.
  • Lokesha, V. and Zhang, Z. -H. The weighted Heron dual mean in n variables, Adv. Stud. Contemp. Math. (Kyungshang) 13 (2), 165–170, 2006.
  • Pe˘cari´c, J. and ˘Simi´c, V. Stolarsky-Tobey mean in n variables, Math. Inequal. Appl. 2 (3), 328–341, 1999. [7] Qi, F. Generalized weighted mean values with two parameters, Proc. Royal Soc. London, Series, Math. Physical Engineering Sci. 454, 2723–2732, 1998.
  • Qi, F. On a two-parameter family of nonhomogeneous mean values, Tamkang J. Math. 29, 155–163, 1998. [9] Stolarsky, K. B. Generalizations of the logarithmic mean, Math. Mag. 48, 87–92, 1975.
  • Xiao, Z. -G. and Zhang, Z. -H. The Henleman mean of n positive numbers, J. Yueyang Normal Univ. 14 (2), 1–5, 2001 (in Chinese).
  • Xiao, Z. -G. and Zhang, Z. -H. The Stolarsky mean of n positive numbers, J. Yueyang Normal Uinv. 14 (4), 5–8, 2001 (in Chinese).
  • Xiao, Z. -G., Zhang, Z. -H., Lokesha, V. and Nagaraja, K. M. A class of new three-parameter generalized weighted means, Int. J. Appl. Math. Stat. 11 (7), 193–202, 2007.
  • Xiao, Z. -G, Zhang, Z. -H., Lokesha, V. and Tang, R. The two-parameter mean of n variables, Int. Rev. Pure Appl. Math. 1 (1), 93–111, 2005.
  • Xiao, Z. -G., Zhang, Z. -H. and Qi, F. A type of mean values of several positive numbers with two parameters, Nonlinear Funct. Anal. Appl. 12, 687–702, 2007.
  • Zhang, Z. -H. Three classes of new means in n+1 variables and their applications, J. Hunan Ed. Inst. 15 (5), 130–136, 1997 (in Chinese).
  • Zhang, Z. -H., Lokesha, V. and Xiao, Z. -G. The weighted Heron mean in n variables, J. Anal. Comput. 1 (1), 57–68, 2005.
  • Zhang, Z. -H., Xiao, Z. -G. and Srivastava, H. M. A general family of weighted elementary symmetric means, Appl. Math. Lett. (2008), doi:10.1016/j.aml.2007.12.030
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İstatistik
Bölüm Matematik
Yazarlar

V. Lokesha Bu kişi benim

Z.-g. Wang Bu kişi benim

Z.-h. Zhang Bu kişi benim

S. Padmanabhan Bu kişi benim

Yayımlanma Tarihi 1 Şubat 2009
Yayımlandığı Sayı Yıl 2009 Cilt: 38 Sayı: 2

Kaynak Göster

APA Lokesha, V., Wang, Z.-g., Zhang, Z.-h., Padmanabhan, S. (2009). THE STOLARSKY TYPE FUNCTIONS AND THEIR MONOTONICITIES. Hacettepe Journal of Mathematics and Statistics, 38(2), 119-128.
AMA Lokesha V, Wang Zg, Zhang Zh, Padmanabhan S. THE STOLARSKY TYPE FUNCTIONS AND THEIR MONOTONICITIES. Hacettepe Journal of Mathematics and Statistics. Şubat 2009;38(2):119-128.
Chicago Lokesha, V., Z.-g. Wang, Z.-h. Zhang, ve S. Padmanabhan. “THE STOLARSKY TYPE FUNCTIONS AND THEIR MONOTONICITIES”. Hacettepe Journal of Mathematics and Statistics 38, sy. 2 (Şubat 2009): 119-28.
EndNote Lokesha V, Wang Z-g, Zhang Z-h, Padmanabhan S (01 Şubat 2009) THE STOLARSKY TYPE FUNCTIONS AND THEIR MONOTONICITIES. Hacettepe Journal of Mathematics and Statistics 38 2 119–128.
IEEE V. Lokesha, Z.-g. Wang, Z.-h. Zhang, ve S. Padmanabhan, “THE STOLARSKY TYPE FUNCTIONS AND THEIR MONOTONICITIES”, Hacettepe Journal of Mathematics and Statistics, c. 38, sy. 2, ss. 119–128, 2009.
ISNAD Lokesha, V. vd. “THE STOLARSKY TYPE FUNCTIONS AND THEIR MONOTONICITIES”. Hacettepe Journal of Mathematics and Statistics 38/2 (Şubat 2009), 119-128.
JAMA Lokesha V, Wang Z-g, Zhang Z-h, Padmanabhan S. THE STOLARSKY TYPE FUNCTIONS AND THEIR MONOTONICITIES. Hacettepe Journal of Mathematics and Statistics. 2009;38:119–128.
MLA Lokesha, V. vd. “THE STOLARSKY TYPE FUNCTIONS AND THEIR MONOTONICITIES”. Hacettepe Journal of Mathematics and Statistics, c. 38, sy. 2, 2009, ss. 119-28.
Vancouver Lokesha V, Wang Z-g, Zhang Z-h, Padmanabhan S. THE STOLARSKY TYPE FUNCTIONS AND THEIR MONOTONICITIES. Hacettepe Journal of Mathematics and Statistics. 2009;38(2):119-28.