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On a generalization of an upper bound for the exponential function

Authors
Bae, Jae GugKim, Seon-Hong
Issue Date
1-May-2009
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Keywords
Upper bound; Exponential function; Polynomials
Citation
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.353, no.1, pp.1 - 7
Journal Title
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume
353
Number
1
Start Page
1
End Page
7
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/13758
DOI
10.1016/j.jmaa.2008.03.034
ISSN
0022-247X
Abstract
With the introduction of a new parameter n, Kim recently generalized an upper bound for the exponential function that implies the inequality between the arithmetic and geometric means. In this paper, we answer some of Kim's conjectures about the inequalities between Kim's generalized upper bound and the original one. We also see the validity of Kim's generalization for some further negative values of x for the case in which the n is rational with both numerator and denominator odd. The range of its validity for negative x is investigated through the study of the zero distribution of a certain family of quadrinomials. (C) 2008 Elsevier Inc. All rights reserved.
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