It should fade eventually. It does depend a little on what the purple was. Directions Plum (in a recent batch) has become notorious for the pink fading out almost straight away and then ending up royal blue that just won't fade. It used to fade a very pretty pink.
As you've said it's fading turquoise, I'm assuming it's not Plum.
You could try a colour remover. It could remove enough of the blue that it doesn't stop the pink being pink. There's several brands in the UK, but avoid anything that's called "stripper" as they're a lot more damaging.