The known results on comparison of extended mean values are used to compare power means, Stolarsky means and Heron mean. Some proofs of well known results are simplified with several new results obtained.
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.
文摘The known results on comparison of extended mean values are used to compare power means, Stolarsky means and Heron mean. Some proofs of well known results are simplified with several new results obtained.
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
文摘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.
