The Arithmetic–Geometric Mean Inequality and the Constant <i>e</i>

Han-sheng, Yang; Yang, Heng

doi:10.1080/0025570x.2001.11953087

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“…Many new estimated values on e have been obtained when researchers study the improvements of the Carleman inequality; see [ 24 – 26 ] for details. We mainly analyze the structural characteristics of I. Schur type inequalities and find out their upper and lower bounds are closely related to the mean value sequences of x n and y n .…”

Section: Introductionmentioning

confidence: 99%

Some Refinements and Generalizations of I. Schur Type Inequalities

Huang

et al. 2014

The Scientific World Journal

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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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Section: Introductionmentioning

confidence: 99%