A stronger inequality of Cîrtoaje's one with power exponential functions
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Authors
Mitsuhiro Miyagi
- General Education, Ube National College of Technology, Tokiwadai 2-14-1, Ube, Yamaguchi 755-8555, Japan.
Yusuke Nishizawa
- General Education, Ube National College of Technology, Tokiwadai 2-14-1, Ube, Yamaguchi 755-8555, Japan.
Abstract
In this paper, we will show that \(a^{2b} + b^{2a} + r (ab(a - b))^2 \leq 1 \) holds for all \(0 \leq a\) and \(0 \leq b\) with \(a + b = 1\)
and all \(0 \leq r \leq\frac{1}{2}\). This gives the first example of a stronger inequality of \(a^{2b} +b^{2a} \leq 1\).
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ISRP Style
Mitsuhiro Miyagi, Yusuke Nishizawa, A stronger inequality of Cîrtoaje's one with power exponential functions, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 3, 224--230
AMA Style
Miyagi Mitsuhiro, Nishizawa Yusuke, A stronger inequality of Cîrtoaje's one with power exponential functions. J. Nonlinear Sci. Appl. (2015); 8(3):224--230
Chicago/Turabian Style
Miyagi, Mitsuhiro, Nishizawa, Yusuke. "A stronger inequality of Cîrtoaje's one with power exponential functions." Journal of Nonlinear Sciences and Applications, 8, no. 3 (2015): 224--230
Keywords
- Power-exponential function
- monotonically decreasing function
- monotonically increasing function.
MSC
References
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