Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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ON A GENERALIZED UPPER BOUND FOR THE EXPONENTIAL FUNCTION

  • Kim, Seon-Hong (Department of Mathematics, Sookmyung Women's University)
  • Received : 2008.11.17
  • Accepted : 2009.02.02
  • Published : 2009.03.31
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Abstract

With the introduction of a new parameter $n{\geq}1$, Kim generalized an upper bound for the exponential function that implies the inequality between the arithmetic and geometric means. By a change of variable, this generalization is equivalent to exp $(\frac{n(x-1)}{n+x-1})\;\leq\;\frac{n-1+x^n}{n}$ for real ${n}\;{\geq}\;1$ and x > 0. In this paper, we show that this inequality is true for real x > 1 - n provided that n is an even integer.

Keywords

References

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