Generalizations and refinements of Hermite-Hadamard's inequality

被引：48
作者：
Qi, F [1 ]
Wei, ZL
Yang, Q
机构：
[1] Henan Polytech Univ, Dept Appl Math & Informat, Res Inst Appl Math, Jiaozuo City 454000, Henan, Peoples R China
[2] Luoyang Normal Coll, Dept Math, Luoyang City 471022, Henan, Peoples R China
[3] N China Inst Water Conservancy & Hydroelect Power, Zhengzhou, Henan, Peoples R China
来源：
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2005年 / 35卷 / 01期
关键词：
harmonic sequence of polynomials; Hermite-Hadamard's inequality; Appell condition; n-convex function; bounded derivative;
D O I：
10.1216/rmjm/1181069779
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article, with the help of the concept of the harmonic sequence of polynomials, the well known Hermite-Hadamard's inequality for convex functions is generalized to cases with bounded derivatives of nth order, including the so-called n-convex functions, from which Hermite-Hadamard's inequality is extended and refined.
引用
收藏
页码：235 / 251
页数：17
相关论文
共 13 条
  • [1] Abramowitz M., 1972, APPL MATH SERIES, V55
  • [2] ALLASIA G, 1999, ATTI ACCAD SCI TORIN, V133, P187
  • [3] [Anonymous], ACTA MATH U COMENIAN
  • [4] [Anonymous], 2003, ADV STUD CONT MATH K
  • [5] CERONE P, 2000, HDB ANAL COMPUTATION
  • [6] Dedic Lj., 2001, J KOREAN MATH SOC, V38, P1235
  • [7] Dragomir S. S., 2000, RGMIA Monographs
  • [8] Guo BN, 2002, J MATH ED SCI TECH, V33, P428, DOI DOI 10.1080/002073902760047913
  • [9] LUO QM, 2002, RGMIA RES REP COLL, V5, P405
  • [10] LUO QM, 2002, RGMIA RES REP COLL, V5, P353
12