5
-This complete the proof.
REMARK 1. - If we set ~(r) = q·r for some q <l, ~ is a contractive
gauge function. It fo11ows that the L.Ciric's Theorem 1 ([2J) is a specia1 case of Theorem 2.
REMARK 2. - We sha11 reca11 that a version of Theorem 2 is given in [3]
by the first author. In [3J one assume conditions which ensure that (1) is true for every Xo in M and (2) is true for a n = n(x) and J
1 ={(O,O)} ,J 2=J3=0.
B I B L I O G R A P H Y
[lJ BROWOER,F.E., Remcvr./u on
6-ixed
pc..<.n.t 06 conbta.c..ti.ve ;t;ype, Nonl inear Anal. Theory Hethods Appl.,3,5(1979), 657-661.[2J CIRIC, L., On mppU1g<l w.U:h a conbta.c..ti.ve UeJLa.-te, Pub1. Inst.Hath.,
Nouve11e serie, 26(40), 1979, 79-82.
[3] CONSERVA, V., Un teolLemo. di ,:unto 6,ù,<lo peJt t!La<I601UllaZi.o.ni.. bU. l.UlO <lpaU.o
un.i.60Jlme eli. Hau.6do1L66 con una UeJuLta. con.tJta.tt.<.va ..Ut ogni. ,:unto (to appear
on Le Matematiche - Catania).
Acc.efto.to peJt
