  The objective of this paper is to (partially) address the issue of finding an
analogue to Khintchine's theorem for IFS Fractals. We study the convergence
case for Diophantine approximations, and show an improved result for higher
dimensions. This matter has been previously studied by Pollington and Velani in
arXiv:math/0401149. Pollington and Velani show a similar result to the one in
this paper (a Khinchine convergence case) and we shall show how our result is
an improvement in the higher dimensional cases.
