In this work, we first discuss some properties of mappings of type $(\gamma)$. Among many other results, we show the compositions of mappings of type $(\gamma)$ is also of type $(\gamma)$ if $\lim_{n\to\infty}n\gamma(\frac tn)>0,$ for some $t>0$. Using these, we obtain a mean ergodic theorem for iterations of a sequence of mappings of type $(\gamma)$ in Banach spaces.
