The log-convexity of the fubini numbers

Abstract

Let $f_n$ denotes the $n$th Fubini number. In this paper, first we give upper and lower bounds for the Fubini numbers $f_n$. Then the log-convexity of the Fubini numbers has been obtained. Furthermore we also give the monotonicity of the sequence ${sqrt[n]{f_n}}_{nge 1}$ by using the aforementioned bounds.