Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON SOME UPPER BOUNDS OF THE EXPONENTIAL FUNCTION

  • Bae, Jae-Gug (Department of Applied Mathematics, Korea Maritime University)
  • Received : 2008.03.24
  • Published : 2008.06.25
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Abstract

In this paper, we introduce some algebraic, rational and polynomial upper bounds of the exponential function on the interval [0,1). And then we compare the acuteness of these bounds.

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References

  1. J. Bae, Optimal polynomial lower bounds for the exponential function, Honam Math. J. 29 (2007), no. 4, 535-542. https://doi.org/10.5831/HMJ.2007.29.4.535
  2. J. Bae, Optimal polynomial lower bounds for the exponential function on rays (to appear).
  3. J. Bae, S-H. Kim, On a generalization of an upper bound for the exponential function (to appear in J. of Math. Analysis and Appl.). https://doi.org/10.1016/j.jmaa.2008.03.034
  4. J. Karamata, Sur l'approximation de $e^x$ par des fonctions rationnelles (in Serbian), Bull. Soc. Math. Phys. Serbie 1 (1949), 7-19.
  5. S-H. Kim, Densely algebraic bounds for the exponential function, Proc. Amer. Math. Soc. 135 (2007), 237-241.
  6. D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, New York, 1970.
  7. W. E. Sewell, Some inequalities connected with exponential function (in Spanish), Rev. Ci (Lima) 40 (1938), 453-456.