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Inequalities of Hadamard Type for r-Convex Functions in Carnot Groups 被引量：3

Inequalities of Hadamard Type for r-Convex Functions in Carnot Groups
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摘要 For a Carnot group G, we establish the relationship between extended mean values and r-convex functions which is introduced in this paper, which is a class of inequalities of Hadamard type for r-convex function on G.
作者 Ming-baoSun Xiao-pingYang
机构地区 DepartmentofAppliedMathematics
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2004年第1期123-132,共10页 应用数学学报（英文版）
基金 Supported in part by SF for Pure Research of Natural Sciences of the Education Department of Hunan Province (No.2000c315) NNSF (No.10271071) and specialized Research Fund for Doctoral Program of Higher Education of China
关键词 r-convex function extended mean values Carnot group INEQUALITY r-convex function extended mean values Carnot group inequality
分类号 O182 [理学—基础数学]
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参考文献10

  • 1Danielli, N.. Garofalo. N., Nhieu, D. Notions of convexity in Carnot groups. Comm. Anal. Geom., 11:263-341 (2003).
  • 2Folland,G.B.,Steill. E.M. Hardy Space on Homogeneous groups. Princeton University Press, Princeton,NJ. 1982.
  • 3Gill,P.M.Pearce.C.E.M..Peearie,J.Hadamard's inequality for r-convex functions.J.Math.Anal.Appl.215:461-470(1997).
  • 4Lu.G.Z.Manfredi.J.J.Stroffolini.B.Convex functions on the Hersenberg group.Cale.Var.Partial Differential Equations.to qppear.
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  • 6Pearce, C.E.M., Pecarie, J. A continuous analogue and an extension of Rado's formulae for convex and concave functions. Bull. Austral. Math. Sot.. 53:229-233 (1996).
  • 7Pearce, C.E.M., Pecarie, J., Simie, V. Stolarsky means and Hadamard's inequality. J. Math. Anal. Appl.,220:99-109 (1998).
  • 8Stolarsky, K,B. Generalization of the logarithmic mean, Math. Mag., 48:87-92 (1975).
  • 9Uhrin, B. Some remarks about the convolution of unimodal functions. Ann. Probab., 12: 640- 645 (1984).
  • 10Yang, G.S., HWang, D.Y. Refinements of Hadamaard's inequality for r-convex functions. Indian J. Pure appl. Math., 32:1571-1579 (2001).

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Acta Mathematicae Applicatae Sinica
2004年 第1期

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