Does the death penalty violate the cruel and unusual punishment clause of the Eighth Amendment? Is it legal to execute someone who has intellectual disabilities? Is it legal to execute someone who is mentally ill?

Death penalty in the United States.

State whether you support or are against the death penalty and why.
Does the death penalty violate the cruel and unusual punishment clause of the Eighth Amendment?
Is it legal to execute someone who has intellectual disabilities?
Is it legal to execute someone who is mentally ill?
Be sure to support your answer with scholarly sources and appellate court opinions.