@article{Nishizawa_Miyagi_2015, title={Extension of an inequality with power exponential functions}, volume={46}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/1831}, DOI={10.5556/j.tkjm.46.2015.1831}, abstractNote={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.}, number={4}, journal={Tamkang Journal of Mathematics}, author={Nishizawa, Yusuke and Miyagi, Mitsuhiro}, year={2015}, month={Dec.}, pages={427–433} }