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Some refinements and generalizations of I. Schur type inequalities.

Authors
  • Gu, Xian-Ming
  • Huang, Ting-Zhu
  • Xu, Wei-Ru
  • Li, Hou-Biao
  • Li, Liang
  • Zhao, Xi-Le
Type
Published Article
Journal
The Scientific World JOURNAL
Publisher
Hindawi (The Scientific World)
Publication Date
Jan 01, 2014
Volume
2014
Pages
709358–709358
Identifiers
DOI: 10.1155/2014/709358
PMID: 24772027
Source
Medline
License
Unknown

Abstract

Recently, extensive researches on estimating the value of e have been studied. In this paper, the structural characteristics of I. Schur type inequalities are exploited to generalize the corresponding inequalities by variable parameter techniques. Some novel upper and lower bounds for the I. Schur inequality have also been obtained and the upper bounds may be obtained with the help of Maple and automated proving package (Bottema). Numerical examples are employed to demonstrate the reliability of the approximation of these new upper and lower bounds, which improve some known results in the recent literature.

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