On Quasi-Gamma Functions

We define the quasi-gamma functions as the functions $f: ]0,\infty[ \longrightarrow ]0,\infty[$ such that $f(1)=1$, $f(x+1)=xf(x)$ for every $x>0$, and $f$ is quasi-convex. The main example of quasi-gamma function is the gamma function defined by Euler. We study some properties of the quasi-gamma functions and of the class ${\emph Q}$ of these functions.