[1] Danielli D, Garofalo N, Nhieu D. Notions of convexity in Carnot groups. Comm Analysis and Geometry, 2003, 11(2): 263--341
[2] Folland G B, Stein E M. Hardy Space on Homogeneous groups. Princeton, NJ: Princeton University Press, 1982
[3] Gill P M, Pearce C E M, Pe\v{c}ari\'{c} J. Hadamard's inequality for r-convex functions. J Math Anal Appl, 1997, 215: 461--470
[4] Guo Baini, Qi Feng. Inequalities for generalized weighted mean values of convex function. Math Inequal Appl, 2001, 4: 195--202
[5] Lu G Z, Manfredi J J, Stroffolini B. Convex functions on the Heisenberg group. Calc Var Partial Differential Equations, 2003, 19: 1--22
[6] Pansu P. Mètriques de Carnot-Carathèodory et quasii-somètries des espacec symètriques de rang un. Ann Math, 1989, 129: 1--60
[7] Pearce C E M, Pe\v{c}ari\'{c} J. A continuous analogue and an extension of Rad\'{o}'s formulae for convex and concave functions. Bull Austral Math Soc, 1996, 53: 229--233
[8] Pearce C E M, Pe\v{c}ari\'{c} J, \v{S}imi\'{c} V. Stolarsky means and Hadamard's inequality. J Math Anal Appl, 1998, 220: 99--109
[9] Qi Feng. Generalized weighted mean values with two parameters. Proceedings of the Royal Society of London Series A-Mathematics, Physical and Engineering Sciences, 1998, 454(1978): 2723--2732
[10] Stolarsky K B. Generalization of the logarithmic mean. Math Mag, 1975, 48: 87--92
[11] Sun Mingbao. Inequalities for two-parameter mean of convex function. Math Practice Theory (in Chinese), 1997, 27: 193--197
[12] Sun Mingbao, Yang Xiaoping. Inequalities of Hadamard type for r-convex functions in Carnot groups. Acta Math Appl Sin, 2004, 20(1): 123--132
[13] Uhrin B. Some remarks about the convolution of unimodal functions. Ann Probab, 1984, 12: 640--645
[14] Yang G S, HWang D Y. Refinements of Hadamaard's inequality for r-convex functions. Indian J Pure Appl Math, 2001, 32: 1571--1579 |