期刊文献+

平方平均与算术平均的差距估计

The Estimation Formulas of Difference in Square Mean and Arithmetic Mean
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摘要 关于n个正数的平方平均与算术平均、几何平均的差的上下界,利用最值压缩定理,给出了两个新的双向不等式. By the compressed independent variables theorem,this paper gives two new double inequalities involving difference in square mean and arithmetic(geometric) mean.
作者 何晓红
出处 《数学的实践与认识》 CSCD 北大核心 2013年第24期285-291,共7页 Mathematics in Practice and Theory
关键词 算术平均 几何平均 平方平均 不等式 最值压缩定理 arithmetic mean geometric mean square mean inequality compressed independent variables theorem
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参考文献10

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二级参考文献11

  • 1D.S.密特利诺维奇.解析不等式[M].张小萍,王龙,译.北京:科学出版社,1987.
  • 2杨克昌.平均值不等式的一个证明与加强.湖南数学通讯,1986,(4):19-20.
  • 3张小明.最值定理与分析不等式.不等式研究通讯,2010,7:107-138.
  • 4Mitrinovic D S. Vasic,P.M.,Analytic Inequalities[M]. Springer-Verlag New York, 1970.
  • 5Cartwright D I, Field M J. A refinement of the arithmetic mean-geometric mean inequality[J]. Proc Amer Math Soc, 1978(71): 36-38.
  • 6bullen P S. Handbook of Means and Their Inequalities[M]. Kluwer Academic Publishers, 2003.
  • 7Mercer A Mcd.Improved upper and lower bounds for the difference of An-Gn[J]. Rocky Mountain J Math, 2001(31): 553-560.
  • 8Williams K S and Beesack P R. Problem 247[J]. Crux Math, 1978(4): 23-26, 37-39.
  • 9Smitrinovic D, Epecaric J, Fink A M. Classical and New Inequalities in Analysis[M]. The Nether- lands: Kluwer Publishers, 19939.
  • 10张小明褚玉明.解析不等式新论[M].哈尔滨:哈尔滨工业大学出版社,2009.

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