TY - JOUR
AU - Nishizawa, Yusuke
AU - Miyagi, Mitsuhiro
PY - 2015/12/22
Y2 - 2024/08/03
TI - Extension of an inequality with power exponential functions
JF - Tamkang Journal of Mathematics
JA - Tamkang J. Math.
VL - 46
IS - 4
SE - Papers
DO - 10.5556/j.tkjm.46.2015.1831
UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/1831
SP - 427-433
AB - 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.
ER -