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L^p空间中的Fejér和Hermite-Hadamard型不等式 被引量:1

Fejér and Hadamard Type Inequalities in L^P Space
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摘要 给出了二阶导数属于Lp空间时Fejér和Hermite-Hadamard型不等式的推广,得到两个新结果. In this paper, Some generalizations of Fejer and Hermite-Hadamard inequality whose second order derivative belongs to Lp space are established.
作者 华云
出处 《数学的实践与认识》 CSCD 北大核心 2012年第13期218-221,共4页 Mathematics in Practice and Theory
基金 山东省高等学校科技计划项目(编号:J11LA57)
关键词 凸函数 积分不等式 Fejér和Hadamard不等式 Convex function integral inequality Fej4r and Hermite-Hadamard inequality
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参考文献7

  • 1Hadamard J. Etude sur les proprietes des fonctions entieres et en particulier d'une fonction consid- eree par Riemann[J]. J Math Pures Appl, 1893(58): 171-215.
  • 2FejEr L. Uberdie fourierreihen, II, Math. Naturwise. Anz Ungar. Akad. Wiss , 1906(24): 369-390.
  • 3Shi Huan-Nan. Two Schur-convex functions related to Hadamard-type integral inequalities[J]. Publ Math Debrecen, 2011, 78(2): 393-403.
  • 4Yang G S, Hwang D Y and Tseng K L. Some inequalities for differentiable convex and concave mappings[J]. Comput Math Appl, 2004(47): 207-216.
  • 5TserNg K L and Wang C S. Some renements of the Fejers inequality for convex functions[J]. Tamsui Oxford J Math Sci, 2005(21): 95-104.
  • 6Dragomir S S. Some error estimates in the trapezoidal quadrature rule[J]. Tamsui Oxford J Math Sci, 2000, 16(2): 259-272.
  • 7Huy V N and Chung N T. Some Generalizations of the FejEr and Hermite-Hadamard inequalities in HSlder spaces[J]. J Appl Math Informatics, 2011, 29(3-4): 859-868.

同被引文献9

  • 1Hadamard J. Etude sur les proprietes des fonctions entreres et en particulier d'une fonction consideree par Riemann[J]. Math. Pures Appl, 1893 (58): 171-215.
  • 2Fej6r L.Uberdie fourierreihen, II, Math. Naturwise. Anz Ungar.Akad.Wiss, 1906(24): 369-390.
  • 3Shi Huan-Nan.Two Schur-convex functions related to Hadamard-type integral inequalities[J]. Publ Math Debrecen, 2011, 78(2): 393-403.
  • 4Yang G S, Hwang D Y and Tseng K L. Some inequalities for differentiable convex and concave mapping[J]. Comput Math Appl, 2004(47): 207-216.
  • 5Tseng K L and Wang C S, Some renements of the Fejdr's inequality for convex functions[J]. Tamsui Oxford J Math Sci, 2005(21): 95-104.
  • 6Dragomir S S. Some error estimates in the trapezoidal quadrature rule[J]. Tamsui Oxford J Math Sci, 2000,16(2): 259-272.
  • 7Yang G S and Tseng K L. Inequalities of Hermite-Hadamard-Fejdr type for convex functions andLipschitizianfunctions[J]. Taiwan Residents J. Math, 2003 7(3): 433-440.
  • 8Yang G Sand K. L. Tseng, On certain integral inequalities related to Hermite-Hadamard inequalities[J]. Math. Anal. Appl., 1999, (239): 180-187.
  • 9Huy V N and Chung N T. Some generalizations of the Fejdr and Hermite-Hadamard inequalities in Hdlder spaces[J]. J Appl Math Inforrnatics, 2011, 29(3-4): 859-868.

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