Apples are not homogenous, the underlying requirement when asking for “equal share” is that no one is dissatisfied with his/her share, or envy someone else’s share. The solution is a dynamic process :

After explaining it clearly to everyone, hover the knife above the left of the first apple as if you were going to cut it through but without doing it, move the knife slowly to the right until one of the three participants says he is happy with that share, cut the apple at that point and that participant gets that share. Then do the same with the second apple and the remaining unserved participants. Whoever doesn’t have anything after that gets the remaining two slices.

Since everyone “could have” spoke earlierto get a share, everyone has a share that they consider the best in their frame of reference and everyone is satisfied.

This solution also works with more than three participants

Edit: I just now realised the goal was to do it in a single cut