Geodesic
A stronger inequality of Cîrtoaje's one with power exponential functions
Miyagi, Mitsuhiro1 ; Nishizawa, Yusuke1
1 General Education, Ube National College of Technology, Tokiwadai 2-14-1, Ube, Yamaguchi 755-8555, Japan
Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 3, p. 224-230.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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 $a^{2b} +b^{2a} \leq 1$.
DOI : 10.22436/jnsa.008.03.06
Classification : 26D10
Keywords: Power-exponential function, monotonically decreasing function, monotonically increasing function.

Miyagi, Mitsuhiro 1 ; Nishizawa, Yusuke 1

1 General Education, Ube National College of Technology, Tokiwadai 2-14-1, Ube, Yamaguchi 755-8555, Japan 
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Miyagi, Mitsuhiro; Nishizawa, Yusuke. A stronger inequality of Cîrtoaje's one with power exponential functions. Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 3, p. 224-230. doi : 10.22436/jnsa.008.03.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.03.06/

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