This complete the proof. REMARK 1. - If we set ~(r) =q·r for some q<l

- 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=J 3=0.
B I B L I OG RA P HY
[lJ
BROWOER,F.E., Remcvr./u on 6-ixed pc..<.n.t 06 conbta.c..ti.ve
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]
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).
CONSERVA, V.,
Un
Acc.efto.to peJt
.ea.
pu.b~ne
<lu palLeJte 6avoILevole del. PILO 6. G. MLlNI
;t;ype,
Nonl inear Anal.