On a generalization of an upper bound for the exponential function
- Authors
- Bae, Jae Gug; Kim, 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
- Pages
- 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
1096-0813
- 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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