Extension of an inequality with power exponential functions

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Published: Dec 22, 2015
DOI: https://doi.org/10.5556/j.tkjm.46.2015.1831
Keywords:
Power-exponential function monotonically decreasing function monotonically increasing function

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Yusuke Nishizawa
Mitsuhiro Miyagi

Abstract

V.\ C\^\i rtoaje et al. \cite{C2009} conjectured and proved \cite{C2011, M2009} that the inequality $a^{rb} + b^{ra} \leq 2$ holds for all nonnegative numbers $r \leq 3$ and nonnegative real numbers $a, b$ with $a +b=2$. In this paper, we will show that $a^{rb} + b^{ra} \leq 2$ holds for all nonnegative $r\geq 3$ and all nonnegative real numbers $a, b$ with $a +b =2$ and some conditions. This gives an extended inequality of conjectured by V.\ C\^\i rtoaje.

Article Details

How to Cite
Nishizawa, Y., & Miyagi, M. (2015). Extension of an inequality with power exponential functions. Tamkang Journal of Mathematics, 46(4), 427–433. https://doi.org/10.5556/j.tkjm.46.2015.1831
Issue
Vol. 46 No. 4 (2015)
Section
Papers
Author Biographies

Yusuke Nishizawa

General Education, Ube National College of Technology, Tokiwadai 2-14-1, Ube, Yamaguchi 755-8555, Japan.

Mitsuhiro Miyagi

General Education, Ube National College of Technology, Tokiwadai 2-14-1, Ube, Yamaguchi 755-8555, Japan.

References

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