numbers98成人网
98成人网 时间:2021-04-11 阅读:(
)
MoosaeiFixedPointTheoryandApplications2014,2014:98http://www.
fixedpointtheoryandapplications.
com/content/2014/1/98RESEARCHOpenAccessCommonxedpointsforsomegeneralizedcontractionpairsinconvexmetricspacesMohammadMoosaei**Correspondence:m.
moosaei@basu.
ac.
irDepartmentofMathematics,Bu-AliSinaUniversity,Hamedan,IranAbstractThepresentstudyfocusesonprovingtheexistenceofcoincidencepointsforself-mappingssatisfyingageneralizedcontractiveconditionwithintheframeworkofconvexmetricspaces.
Theexistenceofcommonxedpointsforweaklycompatibleself-mappingsaswellasBanachoperatorpairsundercertaingeneralizedcontractionsinaconvexmetricspaceisalsoestablished.
MSC:47H09;47H10;47H19;54H25Keywords:Banachoperatorpairs;coincidencepoints;commonxedpoints;compatiblemappings;convexmetricspaces;xedpoints;weaklycompatiblepair1IntroductionandpreliminariesIn,Takahashi[]introducedthenotionofconvexityinmetricspacesandprovedthatallnormedspacesandtheirconvexsubsetsareconvexmetricspaces.
Healsogavesomeexamplesoftheconvexmetricspaceswhicharenotembeddedinanynormed/Banachspaces.
AfterwardGuay,SinghandWhittield[],BegandAzam[],Beg,Azam,AliandMinhas[],ShimizuandTakahashi[],Ciric[],Beg[,],BegandAbbas[],andmanyotherauthorshavestudiedxedpointtheoremsinconvexmetricspaces.
Inthispaper,weintroduce(α,β,γ,η)-generalizedcontractionpairsandstudytheexis-tenceofacoincidencepointforsuchpairsinaconvexmetricspaceundercertaincondi-tions(seeTheorem.
).
Consequently,weprovetheexistenceofacommonxedpointforweaklycompatiblemappingsandalsoBanachoperatorpairswhichare(α,β,γ,η)-generalizedcontractionpairs(seeTheorem.
andTheorem.
).
Wenowreviewnotationsanddenitionsneeded.
WedenotebyNandRthesetofnaturalnumbersandthesetofrealnumbers,respectively.
WealsodenotebyItheidentitymapping.
Inwhatfollows,(X,d)isametricspace,andCisanonemptysubsetofX.
Denition.
LetSandTbetwoself-mappingsofC.
ApointxofCiscalled(i)axedpointofTifTx=x,(ii)acommonxedpointofthepair(S,T)ifSx=Tx=x,and(iii)acoincidencepointofthepair(S,T)ifSx=Tx.
ThesetofxedpointsofTisdenotedbyF(T).
Thesetofcommonxedpoints(respec-tively,coincidencepoints)ofthepair(S,T)isdenotedbyF(S,T)(respectively,C(S,T)).
NotethatC(I,T)=F(T).
Denition.
LetSandTbetwoself-mappingsofC.
ThemappingTiscalled2014Moosaei;licenseeSpringer.
ThisisanOpenAccessarticledistributedunderthetermsoftheCreativeCommonsAttribu-tionLicense(http://creativecommons.
org/licenses/by/2.
0),whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
MoosaeiFixedPointTheoryandApplications2014,2014:98Page2of8http://www.
fixedpointtheoryandapplications.
com/content/2014/1/98(i)acontractionifthereexistsk∈[,)suchthatd(Tx,Ty)≤kd(x,y)forallx,y∈C,(ii)anS-contractionifthereexistsk∈[,)suchthatd(Tx,Ty)≤kd(Sx,Sy)forallx,y∈C,(iii)nonexpansiveifd(Tx,Ty)≤d(x,y)forallx,y∈C,and(iv)S-nonexpansiveifd(Tx,Ty)≤d(Sx,Sy)forallx,y∈C.
Denition.
LetSandTbetwoself-mappingsofC.
Thepair(S,T)issaidtobe(i)commutingifSTx=TSxforallx∈C,(ii)R-weaklycommuting[]ifthereexistsR>suchthatd(STx,TSx)≤Rd(Sx,Tx)forallx∈C.
IfR=,thenthemappingsarecalledweaklycommuting[],(iii)compatible[]iflimn→∞d(STxn,TSxn)=,whenever{xn}∞n=isasequenceinCsuchthatlimn→∞Sxn=limn→∞Txn=xforsomex∈C,and(iv)weaklycompatibleiftheycommuteonC(S,T)i.
e.
STx=TSxforallx∈C(S,T)(see[,]formoredetails).
Itiswellknownthatcommutingmappingsareweaklycommuting,andweaklycommut-ingmappingsareR-weaklymappings.
Moreover,R-weaklymappingsarecompatible,andcompatiblemappingsareweaklycompatible.
Thefollowingexampleshowsthattheconversesoftheaboveresultsarenottrueingeneral.
Example.
LetX=Rwiththeusualmetricd(x,y)=|x–y|forallx,y∈X,wehave:()LetC=[,].
LetSx=xandTx=xforallx∈C.
ItistrivialthatSandTareweaklycommutingbutarenotcommuting.
()LetC=[,∞].
ConsiderSx=x–andTx=xforallx∈C.
ThenSandTare-weaklycommutingbutarenotweaklycommuting(see[]).
()LetC=X,Sx=x,Tx=x,x∈C.
ThenSandTarecompatiblebutarenotR-weaklycommuting(see[,,]formoredetails).
()LetC=[,],anddeneself-mappingsSandTofCbyS()=,S(x)=iforηorη,thenηorηorη<α+γholds.
CompetinginterestsTheauthordeclaresthattheyhavenocompetinginterests.
AcknowledgementsTheauthorisgratefultothereviewersfortheirvaluablecommentswhichimprovedthecontentsofthemanuscript.
Received:28November2013Accepted:27March2014Published:16Apr2014MoosaeiFixedPointTheoryandApplications2014,2014:98Page8of8http://www.
fixedpointtheoryandapplications.
com/content/2014/1/98References1.
Takahashi,T:AconvexityinmetricspacesandnonexpansivemappingI.
KodaiMath.
Semin.
Rep.
22,142-149(1970)2.
Guay,MD,Singh,KL,Whiteld,JHM:Fixedpointtheoremsfornonexpansivemappingsinconvexmetricspaces.
In:ProceedingsofConferenceonNonlinearAnalysis.
LectureNotesinPureandAppliedMathematics,vol.
80,pp.
179-189.
Dekker,NewYork(1982)3.
Beg,I,Azam,A:Fixedpointonstar-shapedsubsetsofconvexmetricspaces.
IndianJ.
PureAppl.
Math.
18,594-596(1987)4.
Beg,I,Azam,A,Ali,F,Minhas,T:Somexedpointtheoremsinconvexmetricspaces.
Rend.
Circ.
Mat.
PalermoXL,307-315(1991)5.
Shimizu,T,Takahashi,W:Fixedpointtheoremsincertainconvexmetricspaces.
Math.
Jpn.
37,855-859(1992)6.
Ciric,L:Onsomediscontinuousxedpointtheoremsinconvexmetricspaces.
Czechoslov.
Math.
J.
43(188),319-326(1993)7.
Beg,I:Structureofthesetofxedpointsofnonexpansivemappingsonconvexmetricspaces.
Ann.
Univ.
MariaeCurie-Skodowska,Sect.
ALII,7-14(1998)8.
Beg,I:Inequalitiesinmetricspaceswithapplications.
Topol.
MethodsNonlinearAnal.
17,183-190(2001)9.
Beg,I,Abbas,M:FixedpointsandbestapproximationinMengerconvexmetricspaces.
Arch.
Math.
41,389-397(2005)10.
Pant,RP:Commonxedpointsofnoncommutingmappings.
J.
Math.
Anal.
Appl.
188,436-440(1994)11.
Sessa,S:Onaweakcommutativityconditionofmappingsinxedpointconsiderations.
Publ.
Inst.
Math.
32,149-153(1982)12.
Jungck,G:Compatiblemappingsandcommonxedpoints.
Int.
J.
Math.
Math.
Sci.
9,771-779(1986)13.
Jungck,G,Rhoades,BE:Fixedpointforsetvaluedfunctionswithoutcontinuity.
IndianJ.
PureAppl.
Math.
29(3),227-238(1998)14.
Chugh,R,Kumar,S:Commonxedpointsforweaklycompatiblemaps.
Proc.
IndianAcad.
Sci.
Math.
Sci.
111,241-247(2001)15.
Jungck,G:Commonxedpointsforcommutingandcompatiblemapsoncompacta.
Proc.
Am.
Math.
Soc.
103,978-983(1988)16.
Jungck,G:CommonxedpointtheoremsforcompatibleselfmapsofHausdortopologicalspaces.
FixedPointTheoryAppl.
3,355-363(2005)17.
Chen,J,Li,Z:Commonxed-pointsforBanachoperatorpairsinbestapproximation.
J.
Math.
Anal.
Appl.
336,1466-1475(2007)18.
Hussain,N:CommonxedpointsinbestapproximationforBanachoperatorpairswithCirictypeI-contractions.
J.
Math.
Anal.
Appl.
338,1351-1363(2008)19.
Agarwal,RP,O'Regan,D,Sahu,DR:FixedPointTheoryforLipschitzian-TypeMappingswithApplications.
Springer,Heidelberg(2009)20.
Hussain,N,Abbas,M,Kim,JK:CommonxedpointandinvariantapproximationinMengerconvexmetricspaces.
Bull.
KoreanMath.
Soc.
48,671-680(2008)21.
Moosaei,M:Fixedpointtheoremsinconvexmetricspaces.
FixedPointTheoryAppl.
2012,ArticleID164(2012).
doi:10.
1186/1687-1812-2012-16410.
1186/1687-1812-2014-98Citethisarticleas:Moosaei:Commonxedpointsforsomegeneralizedcontractionpairsinconvexmetricspaces.
FixedPointTheoryandApplications2014,2014:98
hostslim美国独立日活动正在进行中,针对一款大硬盘荷兰专用服务器:双E5-2620v2/4x 1TB SATA硬盘,活动价60美元月。HostSlim荷兰服务器允许大人内容,不过只支持电汇、信用卡和比特币付款,商家支持7天内退款保证,有需要欧洲服务器的可以入手试试,记得注册的时候选择中国,这样不用交20%的税。hostslim怎么样?HostSlim是一家成立于2008年的荷兰托管服务器商,...
月神科技怎么样?月神科技是由江西月神科技有限公司运营的一家自营云产品的IDC服务商,提供香港安畅、香港沙田、美国CERA、华中电信等机房资源,月神科技有自己的用户群和拥有创宇认证,并且也有电商企业将业务架设在月神科技的平台上。目前,香港CN2云服务器、洛杉矶CN2云主机、华中电信高防vps,月付20元起。点击进入:月神科技官方网站地址月神科技vps优惠信息:香港安畅CN2-GIA低至20元核心:2...
前天,还有在"Hostodo商家提供两款大流量美国VPS主机 可选拉斯维加斯和迈阿密"文章中提到有提供两款流量较大的套餐,这里今天看到有发布四款庆祝独立日的七月份的活动,最低年付VPS主机13.99美元,如果有需要年付便宜VPS主机的可以选择商家。目前,Hostodo机房可选拉斯维加斯和迈阿密两个数据中心,且都是基于KVM虚拟+NVMe整列,年付送DirectAdmin授权,需要发工单申请。(如何...
98成人网为你推荐
苹果appstore宕机苹果手机为什么显示无法连接到appstoreflashfxp注册码找flashfxp3.4注册码台北市cuteftp结点cuteftp抢米网抢小米手机需要下什么软件 速求正大天地网二三线城市适合做生鲜b2b电商吗徐州商标求江苏徐州地区的商标代理机构!discuz伪静态discuz怎么才能把专题目录也实现伪静态的方法详解开源网店免费开源网上商城系统有哪些无忧登陆无忧登录好吗?
域名买卖 .cn域名注册 服务器配置技术网 simcentric isatap 免备案cdn 地址大全 免费ddos防火墙 美国十次啦服务器 电子邮件服务器 789电视 国外代理服务器软件 国外免费asp空间 中国电信宽带测速器 申请免费空间和域名 cdn网站加速 国内空间 黑科云 广州主机托管 建站技术 更多