On a generalization of an upper bound for the exponential function |
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Authors: | Jae Gug Bae |
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Institution: | a Division of Mathematical & Information Science & Semiconductor Physics, College of Engineering, Korea Maritime University, Pusan 606-791, Republic of Korea b Department of Mathematics, College of Science, Sookmyung Women's University, Seoul 140-742, Republic of Korea |
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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. |
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Keywords: | Upper bound Exponential function Polynomials |
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