 In addition to touring the world , Carey performed on a variety of television programs and award shows . After " Fantasy " was released in September throughout Europe , Carey performed the song on the popular British chart show Top of the Pops , which aired live via satellite on Asian television . Carey performed " Fantasy " in France and at the 23rd Annual American Music Awards on January 29 , 1996 . " One Sweet Day " was performed at the 38th Annual Grammy Awards , Princess Diana 's memorial service in September 1997 , and at Carey 's Black Entertainment Television Christmas special in 2001 . During her European promotional tour for the album , Carey performed " Open Arms " on various television programs , including <unk> , <unk> .. ? in Germany , Top of the Pops and Des O 'Connor in the United Kingdom and on Swedish television . 
