A bounded linear operator T on a Banach space X is called a convex-cyclic
operator if there exists a vector xβX such that the convex hull of
Orb(T,x) is dense in X. In this paper, for given an aperiodic element g
in a locally compact group G, we give some sufficient conditions for a
weighted translation operator Tg,wβ:fβ¦wβ fβΞ΄gβ on
Lp(G) to be convex-cyclic. A necessary condition is also
studied. At the end, to explain the obtained results, some examples are given