The answer is in this paper: <i>Yuji Takahashi, Functions with a unique mean value and amenability. Proc. Amer. Math. Soc. 121 (1994), 775-777 </i>  ([Freely accessible here on AMS' site][1])


  [1]: http://www.ams.org/journals/proc/1994-121-03/S0002-9939-1994-1189549-1/home.html