“These are last words, as of one who is about to go away and says 'good-night' or gives his blessing” (Luther). Peace! was the ordinary oriental greeting at parting. Compare Joh 20:21.
My peace I give
Compare 1Jo 3:1. “It is of his own that one gives” (Godet).
Let it be afraid (δειλιάτω)
Only here in the New Testament. Properly it signifies cowardly fear. Rev., fearful. The kindred adjective δειλός fearful, is used by Matthew of the disciples in the storm (Mat 8:26), and in Revelation of those who deny the faith through fear of persecution (Rev 21:8). The kindred noun, δειλία, occurs only in 2Ti 1:7, “God hath not given us the spirit of fear,” contrasted with the spirit of power, love, and a sound mind.