PII: S0019-3577(01)80025-2

ABSTRACT If D is a subset of Ba" and f : D + D is an ei -norm nonexpansive map, then it is known that every bounded orbit off approaches a periodic orbit. Moreover, the minimal period of each periodic point off is boun&d by n! 2", where m = 2"-I. In this paper we shall describe two different procedures to construct periodic orbits of &norm nonexpansive maps. These constructions yield that a lower bound for the largest possible minimal period of a periodic point of an &-norm nonexpansive map is given by 3.2"-i, n > 3. If n 5 5, we shall also improve the upper bound for the largest possible minimal period