  A q-type Holder condition on a function f is given in order to establish
(uniform) convergence of the corresponding basic Fourier series S_q[f] to the
function itself, on the set of points of the q-linear grid. Furthermore, by
adding others conditions, one guaranties the (uniform) convergence of S_q[f] to
f on and "outside" the set points of the q-linear grid.
