Convex-cyclic weighted translations on locally compact groups

A bounded linear operator T on a Banach space X is called a convex-cyclic operator if there exists a vector x is an element of X 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 T-g,T-w : f -> w . f * delta(g) on L-p(G) to be convex-cyclic. A necessary condition is also studied. At the end, to explain the obtained results, some examples are given.