The Hausdorff dimension of the intersection of $\ddot{I}ˆ$-well approximable numbers and self-similar sets

Suxuan Chen

Let $\ddot{I}ˆ:\mathbb{N}\to {\mathbb{R}}_{+}$ be a monotonically non-increasing function, and let $\ddot{I}{ˆ}_v:\mathbb{N}\to {\mathbb{R}}_{+}$ be defined by $\ddot{I}{ˆ}_v(q)=1/q^v$. In this artic…