In the Roman Catholic Church, the first eight days of the Easter Season make up the Octave of Easter and are celebrated as Solemnities of the Lord according to General Norms for the Liturgical Year and Calendar. http://www.catholicculture.org/culture/library/view.cfm?id=5932#EasterGeneral Norms for the Liturgical Year and Calendar.
As each of those days is a Feast of the first order, fasting is clearly inappropriate.
Indeed, because The fifty days from Easter Sunday to Pentecost are celebrated in joyful exultation as one feast day, or better as one "great Sunday," (ibid) it may be inappropriate to fast throughout the Easter season. St Augustine said of Sundays, "Fasting is set aside and prayers are said standing, as a sign of the Resurrection, which is also why the Alleluia is sung on every Sunday". (Ep. 55, 28: CSEL 342, 202)