[[alpha]]凹算子与[[beta]]凸算子之和的多重不动点及其应用.pdf

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1、
J.Sys.Sci.&Math.Scis.27(2)(2007,4),177183αβ ∗(





273165)α(0<α<1)Æβ(β>1)!"#&'αÆβ#MR(2000)()
+47H07,47H10,34B151-./01α4β4
Æ56
47


2、48
![14]#αÆ-β4!"$9$%%&&
:('β4
#);*9<4ββββoo
(+,![5]9-N(y−x)≤Ay−Ax≤M(y−x)(A:P−→P
β4=
$9$%>![68]?%.#)<*
!0[9]9%+
-(β4
=!"$9Æ!",!#@)$9-=!"
%412α(0<α<1)4Aβ(β>1)4:Æ34!0>#.

3、<(/$%56012B+,7E3CDP34
8Banach&'583≤,θ69E5
(E:P+=P−θ.Po6P
)*7DP=+
;$90,='>?
θ≤x≤y,+Fx≤Ny,7,G-
<>@H3DP
=+<;x∈P=x=Ax,I7x3A
=!"7α,β3=A<D:P−→P%-4B'>?x,y∈P,x?r∈(0,1),x∈PFD(rx)≥rDx;I7D3αβDx4:B'>?r∈

4、(0,1),x∈PFD(rx)≤r;I7D3β4αKD3α4
<=-3>'>?s>1,x∈PFD(sx)≤sDx;D3ββ4
<=-3>'>?s>1,x∈PFD(sx)≥sDx.7M⊂E.A:M→EC
F1
?2$9<0≤k<1,='M5>3F1*S,Fa(A(S))≤ka(S),7a(·)69E55@AI7ADB*EFGH7M⊂E,B$9I∈M='>?u∈MC;u≤I,II3M
>DE*67LI

89(10471075)EJFKLI

5、

89(Y2006A04)EG:HLM
N89(20050446001)NO;JOKP8Banach&'2D*EFGH
F?O@ÆVA[1012].,!
P3QR1.171)E8Banach&'PE5
=+DE58WBF>DEI,e>θ;2)A:P−→P189J.
CC
AI≤N.$9A<0>0=(X;Ax≥0Axe,∀x∈P;(1)3)'>3x∈P,Ax≥A1x,

6、Ax≥A2x,5A1:P−→P89J.
$9?0θ,lim>;(2)r→0r0A1eA2:P−→P89J.
$9?t>1FA2(tx)≥g(t)A2x,?2g(t)NA2e>θ,lim>.(3)t→+∞t0A2e∗∗∗∗∗∗∗∗∗IA@)F-=!"xAx,,Gx<1<x,x≥k1e,x≥k2e.5N3DP
=+<k1,k23=<S1C3DE4-(1)

7、,G
αβ9Q1.15h(r)=r(0<α<1),g(t)=t,(β>1)YZFF([
TU1.17Q1.15
-1),2)!R-3)G33)'>3x∈P,Ax≥A1x,Ax≥A2x.4A1:P−→P89J.
α4(0<α<1),A1e>θ;A2:P−→P89J∗∗∗∗∗∗.β4(β>1),A2e>θ;IA@)F-=!"xAx,?2x<1<x,x∗≥ke,x∗∗≥ke.125N3DP
=+<k1,k23=<S2SA=A1+A2YAx≥

8、A1x,Ax≥A2x;Aα4Aβ4:ÆQR1.2ZF71)E38Banach&'PE5
=+D=+<3N;2)4A1:P−→Pα4(0<α<1);A2:P−→Pβ4(β>1);3)A:P−→P%-DB*EFGH(CCGH),2'>3x∈P,Ax≥A1x,Ax≥A2x.4)sup{Ax

9、x=1}<1,inf{Ax

10、x=1}>0,inf{Ax

11、x=1}>0,N12IA@∗∗∗∗∗∗)F-=!"xAx,?2x<1<x.