On shrinking targets for piecewise expanding interval maps

For a map (Formula presented.) with an invariant measure (Formula presented.), we study, for a (Formula presented.)-typical (Formula presented.), the set of points (Formula presented.) such that the inequality (Formula presented.) is satisfied for infinitely many (Formula presented.). We give a formula for the Hausdorff dimension of this set, under the assumption that (Formula presented.) is piecewise expanding and (Formula presented.) is a Gibbs measure. In some cases we also show that the set has a large intersection property.