Capital punishment is defined as one person taking the life of another consciously,
that is the definition of murder. Murdering is wrong, death is not a solution for anything. Even though we are all humans and we all make mistakes some actions have to be punished. It won't be fair if someone robbed a person and nothing happened, that action has to have a punishment for shure. But that punishment should not be killing him. Humans can not go through life killing people because they did something wrong, that would be extremely bloody and disgusting. There are other steps society can take before we get that far. There may be penalties depending on the crimes committed, it would increase the severity of the punishment depending on the gravity of the crime.
Another different case would be if someone kills another person, should that person have a capital punishment? No, of course not. Beyond that he is a murderer and that he doesn't deserve to live, after all the damage he have done, he is still a person, just like everybody, and has the right of living just like you. Moreover it would be completely contradictory, “do not kill because you are gonna be killed” it won't make sense at all.
In my opinion, i believe serial killers should obviously get a punishment for what they have done, but no death, they should go to prison for their entire life, there they should be alone, they shouldn't leave them the chance to have visits, not even their family, the only thing they should have at their fingertips is a psychological help and food.