TY - JOUR
AU - Qi, Feng
AU - Luo, Qiu-Ming
PY - 2000/06/30
Y2 - 2024/08/03
TI - Generalization of H. Minc and L. Sathre's inequality
JF - Tamkang Journal of Mathematics
JA - Tamkang J. Math.
VL - 31
IS - 2
SE - Papers
DO - 10.5556/j.tkjm.31.2000.406
UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/406
SP - 145-148
AB - An inequality of H. Minc and L. Sathre (Proc. Edinburgh Math. Soc. ${\bf 14}$(1964/65), 41-46) is generalized as follows: Let $n$ and $m$ be natural numbers, $k$ a nonnegative integer, then we have<br />$${n+k\over n+m+k}<{{\root n\of {(n+k)!/k!}}\over {\root {n+m}\of {(n+m+k)!/k!}}}<1.$$<br />From this, some corollaries are deduced. At last, an open problem is proposed.
ER -