• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Common Fixed Points for a Countable Family of Non-self Mappings in Cone Metric Spaces with the Convex Property

    2014-07-31 22:37:08PIAOYongjieLIChunhua

    PIAO Yong-jie,LI Chun-hua

    (College of Science,Yanbian University,Yanji 133002,China)

    Common Fixed Points for a Countable Family of Non-self Mappings in Cone Metric Spaces with the Convex Property

    PIAO Yong-jie,LI Chun-hua

    (College of Science,Yanbian University,Yanji 133002,China)

    A new common f i xed point result for a countable family of non-self mappings def i ned on a closed subset of a cone metric space with the convex property is obtained,and from which,a more general result is given.Our main results improve and generalize many known common f i xed point theorems.

    common f i xed point;the convex property;cone metric space

    §1.Introduction and Preliminaries

    Huang and Zhang[1]recently have introduced the concept of cone metric spaces,where the set of real number is replaced by an ordered Banach space,and they have established some fi xed point theorems for a contractive type mapping on a normal cone metric space. Subsequently,some other authors[27]have generalized the results of Huang and Zhang[1]and have studied the existence of common fi xed points of a fi nite family of self mappings satisfying a contractive type condition in the framework of normal or non-normal cone metric spaces.In [8],the authors discussed some common fi xed point problems of a pair of non-self mappings de fi ned on a nonempty closed subset of a non-normal cone metric space.On the other hand, the authors recently have discussed and obtained some unique existence theorems of common fi xed points for a countable family of mappings on 2-metric spaces or metrically convex metric spaces respectively,see[9-12].

    In this paper,we will give some common f i xed point theorems for a countable family of non-self mappings def i ned on a nonempty closed subset of a non-normal cone metric space with the convex property.

    Let E be a real Banach space.A subset P0of E is called a cone if and only if

    (i)P0is closed,nonempty and P0/={0};

    (ii)a,b∈?,a,b≥0 and x,y∈P0implies ax+by∈P0;

    (iii)P0∩(?P0)={0}.

    Given a cone P0?E,we def i ne a partial ordering≤on E with respective to P0by x≤y if and only if y?x∈P0.We will write x<y to indicate that x≤y but x/=y,while x?y will stand for y?x∈int P0(the interior of P0).

    The cone P0is called normal if there is a number L>0 such that for all x,y∈E,

    The least positive number satisfying the above is then called the normal constant of P0.

    Let X be a nonempty set.Suppose that the mapping d:X×X→E satisf i es

    (d1)0≤d(x,y)for all x,y∈X and d(x,y)=0 if and only if x=y;

    (d2)d(x,y)=d(y,x)for all x,y∈X;

    (d3)d(x,y)≤d(x,z)+d(z,y),for all x,z,y∈X.

    Then d is called a cone metric on X and(X,d)is called a cone metric space.

    Let(X,d)be a cone metric space.We say that{xn}?X is

    (e)Cauchy sequence if for every c∈E with 0?c,there is an N such that for all n,m>N, d(xm,xn)?c;

    (f)Convergent sequence if for every c∈E with 0?c,there is an N such that for all n>N such that d(xn,x)?c for some x∈E.In this case,we say that x is the limit of{xn}and

    A cone metric space X is said to be complete if every Cauchy sequence in X is convergent in X.

    A cone metric space X is said to have the convex property if for each nonempty closed subset C of X and each x∈C and y/∈C,there exists a point z∈?C such that

    A metric space is said to be metrically convex[1314],if for any x,y∈with x/=y,there exists a point z∈X such that d(x,z)+d(z,y)=d(x,y).

    Lemma 1[14]If K is a nonempty closed subset of a complete metrically convex space, then for any x∈K and y/∈K,there exists a point z∈?K such that

    The above Lemma 1 shows that a complete metrically convex space is the example of a cone metric spaces with the convex property.

    Lemma 2[8]Let(X,d)be a cone metric space.Then the following properties are often useful(particulary when dealing with cone metric spaces in which the cone needs not to be normal)

    (P1)If u≤v and v?w,then u?w;

    (P2)If 0≤u?c for each c∈intP0,then u=0;

    (P3)If x≤y+c for each c∈intP0,then x≤y;

    (P4)If 0≤x≤y and a∈? with a≥0,then 0≤ax≤ay;

    (P5)If 0≤xn≤ynfor each n∈? and limn→∞xn=x,limn→∞yn=y,then 0≤x≤y;

    (P6)If E is real Banach space with a cone P0and a≤λa where a∈P0and 0<λ<1, then a=0;

    (P7)If c∈intP0,0≤anand an→0,then there exists n0such that for all n>n0,we have an?c.

    Remark 1It follows from(P7)that the sequence xnconverges to x∈X if d(xn,x)→0 as n→∞and xnis a Cauchy sequence if d(xn,xm)→0 as n,m→∞.In the case when the cone is not necessarily normal,we have only one half of the statements of Lemma 1 and Lemma 4 from[1].

    The following is a particular form of the well-known result in[15].

    Lemma 3Let(X,d)be a cone metric space with a cone P0,{xn}a sequence in X and {an}a sequence in P0and an→0.If for any m>n>1,d(xn,xm)≤an,then{xn}is a Cauchy sequence.

    §2.Main Results

    Theorem 1Let K be a nonempty complete and closed subset of a cone metric space X with the convex property,{Ti:K→X}i∈?a family of non-self mappings satisfying that there exists λ∈(0,)such that for each x,y∈K and i,j∈? with i/=j,

    where

    If Ti(x)∈K for all x∈?K and i∈?,then{Ti}i∈?have a unique common fi xed point in K.

    ProofTake x0∈K.We will construct two sequences{xn}and{in the following manner.De fi ne=T1x0.If∈K,then put x1=∈/K,then by the convex property of X,there exists x1∈?K such that d(x0,x1)+d()=d().De fi ne=T2x1.If∈K,then put x2=∈/K,then by the convex property of X,there exists x2∈?K such that d(x1,x2)+d()=d().Continuing this way,we obtain{xn}and{x′n}

    where

    hence

    hence

    Case IIIf xn∈P and xn+1∈Q,then=Tn+1xn. Hence

    where

    un,n+1(xn?1,xn)

    hence

    hence

    where

    By Case II,we obtain that

    hence we obtain that

    By Case II again,we have

    hence

    But d(xn,xn+1)≤d(xn?1,+dn+1),hence we obtain that

    and therefore

    By Case II again,we have

    or

    and therefore for any n∈? with n≥2,

    or

    So,for any n∈? with n≥2,

    Let δ=h?1[d(x2,x1)+d(x1,x0)]and K=h12,then K<1,δ∈P0and for all m>n≥2,

    By the properties of P and Q,we can see that there are in fi nite elements xnk+1∈{xn}such that xnk+1∈P.

    For any fi xed n∈?,there exists an enough large k∈? such that nk+1>n and xnk+1∈P. And we can obtain the following

    where

    If un,nk+1(x?,xnk)=d(x?,xnk),then for any c∈intP0,there exists a large k0∈? such that for k≥k0,

    Hence

    and therefore,for any c∈intP,there exists a large k0∈? such that for k≥k0,

    Hence we get that d(Tnx?,x?)?c for all c∈intP,so by Lemma 2(P2),Tnx?=x?for all n∈?.This means that x?is a common f i xed point of{Tn}n∈?.

    Suppose that p and q are all common f i xed points of{Tn}n∈?,then

    If u1,2(p,q)=d(p,q),then d(p,q)≤λd(p,q),hence d(p,q)=0 by Lemma 2(P6)and therefore p=q;

    Hence x?is the unique common fi xed point of{Tn}n∈?.

    Remark 2If K=X itself is complete,then the boundary condition is super fl ous.In this case,we can easily know that xn=x′n,hence the convex structure of X is also super fl ous.

    Remark 3In fact,the condition“i/=j”in Theorem 1 can be replaced by the weaker condition“i<j”.

    Remark 4Many authors in the references and others obtained many common fi xed point theorems only for a fi nite family of mappings,but we fi rst introduced the concept of the convex property to discuss the existence of common fi xed point for a countable family of non-self-mappings on cone metric spaces in Theorem 1.Since we treat non-self-mappings,we need to consider the boundary condition of the given closed subset K of X in Theorem 1.The boundary condition in Theorem 1 is very weaker than that in[8]and very di ff erent from that in[8].So,we think that our technique is very di ff erent from the previous ones and our method is new.

    Theorem 2Let K a nonempty complete and closed subset of a cone metric space(X,d) with the convex property,{Ti,j:X→X}i,j∈?a family ofmappings,{mi,j}i,j∈?a family of positive integral numbers such that there exists λ∈(0,)such that for each x,y∈X and i1,i2,j∈? with i1/=i2,

    where

    Furthermore,if(a)for each i,j∈?,(?K)?K,(b)for each i1,i2,μ,ν∈? withμ/=ν, Ti1,μTi2,ν=Ti2,νTi1,μ.Then{Ti,j}i,j∈?has a unique common fi xed point in K.

    where

    If ui,k,j(Ti,j(pj),Ti,j(pj))=0,then d(Ti,j(pj),Sk,j(Ti,j(pj)))≤λ0=0,hence d(Ti,j(pj), Sk,j(Ti,j(pj)))=0,i.e.,Ti,j(pj)=Sk,j(Ti,j(pj));

    Hence in any situation,we have that Ti,j(pj)is a fi xed point of Sk,jfor each k with k/=i. So Ti,j(pj)is a common fi xed point of{Si,j}i∈?.By uniqueness of common fi xed points of {Si,j}i∈?,we haveTi,j(pj)=pjfor each i∈?.Hence pjis a common fi xed point of{Ti,j}i∈?.

    If ujand vjare common fi xed points of{Ti,j}i∈?,then they are also common fi xed points of{Si,j}i∈?,hence ui=pj=vj.So j∈?,{Ti,j}i∈?has a unique common fi xed point pj.

    Finally,we will prove that{Ti,j}i,j∈?has a unique common fi xed point.Now,we prove that for eachμ,ν∈?,pμ=pν.In fact,for any i1,i2,μ,ν∈? withμ/=ν,since Ti1,μ(pμ)=pμand Ti2,ν(pν)=pν,Ti1,μ(Ti2,ν(pν))=Ti1,μ(pν),hence Ti2,ν(Ti1,μ(pν))=Ti1,μ(Ti2,ν(pν))=Ti1,μ(pν) by(b).This means that Ti1,μ(pν)is a fi xed point of Ti2,νfor each i2,i.e.,Ti1,μ(pν)is a common fi xed point of{Ti2,ν}i2∈?.But{Ti2,ν}i2∈?has a unique common fi xe point pν,hence Ti1,μ(pν)=pνfor each i1and therefore pνis a common fi xed point of{Ti1,μ}i1∈?.But {Ti1,μ}i1∈?has a unique common fi xed point pμ,hence pμ=pν.Let p?=pj,then p?is thecommon f i xed point of{Ti,j}i,j∈?.The uniqueness of common f i xed points of{Ti,j}i,j∈?is obvious.

    Remark 5In Theorem 2,the domain of{Ti,j}i,j∈?must be X.In fact,we can not be sure that Ti,j(pj)∈K even if pj∈K in the proof of Theorem 2.Hence we should not suppose that the domain of{Ti,j}i,j∈?is K.

    [1]HUANG Long-guo,ZHANG Xian.Cone metric spaces and f i xed point theorems of contractive mappings[J]. J Math Anal Appl,2007,332(2):1468-1476.

    [2]ABBAS M,JUNGCK G.Common f i xed point results for noncommuting mappings without continuity in cone metric spaces[J].J Math Anal Appl,2008,341(1):416-420.

    [3]ABBAS M,RHOADES B E.Fixed and periodic point results in cone metric spaces[J].Applied Math Letters, 2009,22(4):511-515.

    [4]RAJA P,VAEZPOUR S M.Some extensions of Banach’s contraction principle in complete cone metric spaces[J].Fixed point theory and Applications,2008,Article ID 768294,11 pages.

    [5]KADELBURG Z,RADENO′VIC S,ROSI′C B.Strict contractive conditions and common f i xed point theorems in cone metric spaces[J].Fixed point theory and Applications,2009,Article ID 173838,14 pages.

    [6]JUNGCK G,RADENO′VIC S,RADOJE′VIC S,et al.Common f i xed point theorems for weakly compatible pairs on cone metric spaces[J].Fixed point theory and Applications,2009,Article ID 643840,13 pages.

    [7]ILI′C D,RAKO?CEVI′C V.Quasi-contraction on a cone metric space[J].Applied Math Letters,2009,22(5): 728-731.

    [8]JANKO′VIC S,KADELBURG Z,RADENO′VIC S,et al.Assad-Kirk-Type f i xed point theorems for a pair of non-self mappings on cone metric spaces[J].Fixed point theory and Applications,2009,Article ID 7610386, 16 pages.

    [9]PIAO Yong-jie.Unique common f i xed point theorems for a family of non-self maps in metrically convex spaces[J].Mathematica Applicata,2009,22(4):852-857.

    [10]PIAO Yong-jie.Unique common f i xed point theorems for a family of quasi-contractive type maps in metrically convex spaces[J].Acta Mathematica Scientica,2010,30A(2):485-493(in Chinese).

    [11]PIAO Yong-jie.Unique common f i xed point theorems for a family of self-maps with same type contractive condition in 2-metric spaces[J].Anal Theo Appl,2008,24(4):316-320.

    [12]PIAO Yong-jie.Unique common f i xed point theorems for a family of self-maps with same quasi-contractive type condition in 2-metric spaces[J].J of Nanjing Univ Math Biquart,2010,27(1):82-87(in Chinese).

    [13]ASSAD N A,KIRK W A.Fixed point theorems for set-valued mappings of contractive type[J].Pacif i c J Math,1972,43:553-562.

    [14]KHAN M S,PATHAK H K,KHAN M D.Some f i xed point theorems in metrically convex spaces[J].Georgain J Math,2000,7(3):523-530.

    [15]AZAM A,BEG I,ARSHAD M.Fixed point in topological space valued cone metric spaces[J].Fixed Point Theory and Applications,2010,Article ID 604084,9 pages.

    tion:47H05,47H10

    CLC number:O189.1,O177.91Document code:A

    1002–0462(2014)02–0221–10

    date:2012-07-19

    Supported by the National Natural Science Foundation of China(11361064)

    Biographies:PIAO Yong-jie(1962-),male(Chaoxianzu),native of Jiutai,Jilin,a professor of Yanbian University,Ph.D.,engages in nonlinear theory and space theory;LI Chun-hua(1975-),female(Chaoxianzu),native of Baishan,Jilin,a lecturer of Yanbian University,Ph.D.,engages in functional analysis and space theory.

    国产精品一区www在线观看| 国产在视频线在精品| 联通29元200g的流量卡| 寂寞人妻少妇视频99o| 日韩精品有码人妻一区| 91精品伊人久久大香线蕉| 国产中年淑女户外野战色| 天堂影院成人在线观看| 免费无遮挡裸体视频| 国产精品国产三级专区第一集| 99久久中文字幕三级久久日本| 乱人视频在线观看| 国产69精品久久久久777片| 精品久久久久久久人妻蜜臀av| 国产av码专区亚洲av| 村上凉子中文字幕在线| 综合色丁香网| 亚洲精品456在线播放app| 18+在线观看网站| 亚洲电影在线观看av| 久久这里只有精品中国| av卡一久久| 亚洲国产成人一精品久久久| 欧美激情久久久久久爽电影| 国产一区二区在线观看日韩| 亚洲国产精品成人综合色| 麻豆av噜噜一区二区三区| 赤兔流量卡办理| 91久久精品电影网| 91久久精品国产一区二区三区| 国产老妇伦熟女老妇高清| 老女人水多毛片| 国产精品一区二区在线观看99 | 欧美日韩一区二区视频在线观看视频在线 | 大香蕉97超碰在线| 日韩视频在线欧美| 日韩av在线免费看完整版不卡| 亚洲国产欧美在线一区| 亚洲国产色片| 麻豆一二三区av精品| 亚洲精品aⅴ在线观看| 国产精品人妻久久久影院| 亚洲五月天丁香| 久热久热在线精品观看| 少妇高潮的动态图| 七月丁香在线播放| 亚洲国产精品成人久久小说| 亚洲在线观看片| 日本黄色视频三级网站网址| 久久精品影院6| 一本一本综合久久| 国产欧美日韩精品一区二区| 国产乱人视频| av在线天堂中文字幕| 免费黄色在线免费观看| 日日摸夜夜添夜夜添av毛片| 欧美日韩精品成人综合77777| 欧美3d第一页| 岛国毛片在线播放| 国产精品,欧美在线| av国产久精品久网站免费入址| 99久国产av精品| 国产成人freesex在线| 国产精品无大码| 一级毛片久久久久久久久女| 特大巨黑吊av在线直播| 一级黄色大片毛片| 欧美精品国产亚洲| 午夜激情福利司机影院| 久久精品国产亚洲av涩爱| 黄片无遮挡物在线观看| 亚洲aⅴ乱码一区二区在线播放| 国产精品久久久久久久久免| 三级男女做爰猛烈吃奶摸视频| 国产伦精品一区二区三区视频9| 免费搜索国产男女视频| 观看免费一级毛片| 日本-黄色视频高清免费观看| 国产精品一区二区三区四区久久| 久久精品夜色国产| 麻豆成人av视频| 国产精品无大码| 日本av手机在线免费观看| 成人亚洲精品av一区二区| 99久久九九国产精品国产免费| 男人舔女人下体高潮全视频| 18禁在线无遮挡免费观看视频| 亚洲国产精品国产精品| 精品一区二区三区人妻视频| 嫩草影院精品99| 建设人人有责人人尽责人人享有的 | 亚洲av日韩在线播放| 中文精品一卡2卡3卡4更新| 国产精品嫩草影院av在线观看| 中文字幕久久专区| 久久99精品国语久久久| av视频在线观看入口| 成人亚洲精品av一区二区| 看十八女毛片水多多多| 欧美精品国产亚洲| 久久精品夜色国产| 99久久九九国产精品国产免费| 菩萨蛮人人尽说江南好唐韦庄 | 国产精品一区二区三区四区免费观看| 亚洲av男天堂| 久久久久网色| 国产精品99久久久久久久久| www.色视频.com| 日本一二三区视频观看| 联通29元200g的流量卡| 精品人妻视频免费看| 岛国在线免费视频观看| 男女那种视频在线观看| 蜜臀久久99精品久久宅男| 免费看美女性在线毛片视频| 直男gayav资源| 欧美三级亚洲精品| or卡值多少钱| 亚洲久久久久久中文字幕| av天堂中文字幕网| 亚洲国产欧美人成| 久久精品国产99精品国产亚洲性色| 日韩,欧美,国产一区二区三区 | av专区在线播放| 波多野结衣高清无吗| 日本免费a在线| 午夜福利成人在线免费观看| 午夜福利网站1000一区二区三区| 嫩草影院新地址| 直男gayav资源| 1000部很黄的大片| 免费大片18禁| 久热久热在线精品观看| 国产午夜福利久久久久久| 男女边吃奶边做爰视频| 女的被弄到高潮叫床怎么办| 天堂中文最新版在线下载 | 久久久亚洲精品成人影院| 中文字幕熟女人妻在线| 直男gayav资源| 我的老师免费观看完整版| 丰满乱子伦码专区| 成年av动漫网址| 美女脱内裤让男人舔精品视频| 国产高清视频在线观看网站| 秋霞在线观看毛片| 欧美最新免费一区二区三区| 久久精品综合一区二区三区| 亚洲不卡免费看| 国产午夜福利久久久久久| 欧美性猛交黑人性爽| 成人鲁丝片一二三区免费| 一个人看的www免费观看视频| 一本—道久久a久久精品蜜桃钙片 精品乱码久久久久久99久播 | 国产成人精品婷婷| 国产一级毛片在线| 日本黄大片高清| 91久久精品国产一区二区三区| 亚洲精品456在线播放app| 欧美日韩综合久久久久久| 国产一区二区亚洲精品在线观看| 亚洲久久久久久中文字幕| 午夜福利在线观看免费完整高清在| 欧美性猛交黑人性爽| 中文字幕制服av| 欧美区成人在线视频| 日本猛色少妇xxxxx猛交久久| a级毛色黄片| 色综合色国产| 丰满乱子伦码专区| 国产 一区 欧美 日韩| 在线观看av片永久免费下载| 精品久久久久久久末码| 美女被艹到高潮喷水动态| 日本与韩国留学比较| 欧美成人一区二区免费高清观看| 国产精品不卡视频一区二区| 免费电影在线观看免费观看| 婷婷色av中文字幕| 久久热精品热| 97热精品久久久久久| av专区在线播放| 黄片wwwwww| 午夜福利视频1000在线观看| 免费看光身美女| 国产精品一及| 晚上一个人看的免费电影| 老司机影院毛片| 高清av免费在线| 国产单亲对白刺激| 亚洲精品aⅴ在线观看| 国产黄片视频在线免费观看| 成人欧美大片| 久久久成人免费电影| 国产成人aa在线观看| 国产成人freesex在线| 亚洲av福利一区| 美女高潮的动态| 久久精品影院6| 晚上一个人看的免费电影| 日本黄大片高清| 我要看日韩黄色一级片| 亚洲av成人精品一区久久| 亚洲欧美日韩无卡精品| 国产精品久久久久久av不卡| 尾随美女入室| av又黄又爽大尺度在线免费看 | 国产免费一级a男人的天堂| 听说在线观看完整版免费高清| 高清在线视频一区二区三区 | 91精品伊人久久大香线蕉| av专区在线播放| 免费播放大片免费观看视频在线观看 | 一级爰片在线观看| 欧美bdsm另类| 国产精品国产三级国产专区5o | 99久国产av精品国产电影| 欧美日韩国产亚洲二区| 亚洲内射少妇av| 亚洲欧美精品综合久久99| 日本黄大片高清| 一夜夜www| 啦啦啦观看免费观看视频高清| eeuss影院久久| 乱系列少妇在线播放| 国产毛片a区久久久久| 变态另类丝袜制服| 老女人水多毛片| 少妇人妻一区二区三区视频| 最近的中文字幕免费完整| 网址你懂的国产日韩在线| 国产精品三级大全| 成年免费大片在线观看| 91午夜精品亚洲一区二区三区| 一个人观看的视频www高清免费观看| av专区在线播放| 日韩制服骚丝袜av| 亚洲精品456在线播放app| 我的老师免费观看完整版| 日日摸夜夜添夜夜爱| 一级毛片aaaaaa免费看小| 久久精品国产自在天天线| 国产成人aa在线观看| 夫妻性生交免费视频一级片| 欧美zozozo另类| 免费观看精品视频网站| 色综合亚洲欧美另类图片| 青春草国产在线视频| 国产老妇女一区| 美女xxoo啪啪120秒动态图| 丝袜喷水一区| 色综合亚洲欧美另类图片| 免费看av在线观看网站| 日韩av在线免费看完整版不卡| 日韩高清综合在线| 国产成人freesex在线| 亚洲欧洲日产国产| 天堂网av新在线| 少妇人妻一区二区三区视频| 青春草国产在线视频| 大话2 男鬼变身卡| 免费搜索国产男女视频| 久久鲁丝午夜福利片| 国产黄a三级三级三级人| 亚洲美女搞黄在线观看| 黄片wwwwww| 人妻系列 视频| 大话2 男鬼变身卡| 性色avwww在线观看| 久久久久久久久久成人| or卡值多少钱| 黄色欧美视频在线观看| av免费在线看不卡| 日本三级黄在线观看| 只有这里有精品99| 一本一本综合久久| 精品熟女少妇av免费看| 一边摸一边抽搐一进一小说| 波野结衣二区三区在线| 欧美zozozo另类| 中国美白少妇内射xxxbb| 国产精品一区二区三区四区久久| 久久人妻av系列| 看非洲黑人一级黄片| 精品无人区乱码1区二区| 日本黄色视频三级网站网址| 久久久久九九精品影院| 老司机影院毛片| 91在线精品国自产拍蜜月| 波多野结衣巨乳人妻| 国产一区亚洲一区在线观看| 欧美另类亚洲清纯唯美| 精华霜和精华液先用哪个| 久久精品夜色国产| 亚洲精品乱码久久久久久按摩| 国内精品宾馆在线| 国产精品久久久久久久电影| 毛片一级片免费看久久久久| 欧美不卡视频在线免费观看| 国产高清有码在线观看视频| 熟妇人妻久久中文字幕3abv| av在线天堂中文字幕| 看片在线看免费视频| 国产精品,欧美在线| 高清毛片免费看| 亚洲成人精品中文字幕电影| 成人鲁丝片一二三区免费| 日韩av不卡免费在线播放| 国产精华一区二区三区| 日本-黄色视频高清免费观看| 亚洲婷婷狠狠爱综合网| av福利片在线观看| 亚洲精品影视一区二区三区av| 高清视频免费观看一区二区 | 51国产日韩欧美| 久久精品91蜜桃| av卡一久久| 国内精品一区二区在线观看| 欧美激情在线99| 伦精品一区二区三区| 久久婷婷人人爽人人干人人爱| 国产人妻一区二区三区在| 天堂中文最新版在线下载 | 国产av码专区亚洲av| 99久久无色码亚洲精品果冻| 伦精品一区二区三区| 狂野欧美激情性xxxx在线观看| 成人综合一区亚洲| АⅤ资源中文在线天堂| 免费观看精品视频网站| 精品久久国产蜜桃| 精品久久久久久久人妻蜜臀av| 高清av免费在线| 国产成人精品一,二区| 国产成人免费观看mmmm| 国产亚洲av片在线观看秒播厂 | 变态另类丝袜制服| 久久久精品大字幕| 天堂√8在线中文| 国产色爽女视频免费观看| 婷婷六月久久综合丁香| av线在线观看网站| 美女国产视频在线观看| 国产乱人偷精品视频| 男女下面进入的视频免费午夜| 国产v大片淫在线免费观看| 日本与韩国留学比较| 三级国产精品片| 1000部很黄的大片| 亚洲欧美日韩高清专用| 你懂的网址亚洲精品在线观看 | 午夜福利网站1000一区二区三区| 成人性生交大片免费视频hd| 中文字幕av成人在线电影| 日韩亚洲欧美综合| 麻豆久久精品国产亚洲av| 春色校园在线视频观看| 我的老师免费观看完整版| 精品欧美国产一区二区三| 日本-黄色视频高清免费观看| 最近手机中文字幕大全| 三级国产精品欧美在线观看| 精品一区二区三区视频在线| 久久精品人妻少妇| 青春草国产在线视频| 日本五十路高清| 在线免费观看不下载黄p国产| 美女大奶头视频| 麻豆av噜噜一区二区三区| 欧美日本亚洲视频在线播放| 女人被狂操c到高潮| 欧美日韩在线观看h| 桃色一区二区三区在线观看| 日本与韩国留学比较| 美女高潮的动态| 亚洲真实伦在线观看| 国产中年淑女户外野战色| 久久久午夜欧美精品| 亚洲人与动物交配视频| 国产三级在线视频| 超碰97精品在线观看| 村上凉子中文字幕在线| 午夜精品国产一区二区电影 | 夫妻性生交免费视频一级片| 午夜老司机福利剧场| 高清午夜精品一区二区三区| 男插女下体视频免费在线播放| 精品熟女少妇av免费看| 在现免费观看毛片| 日韩av在线免费看完整版不卡| 亚洲欧美一区二区三区国产| 亚洲成人av在线免费| 欧美成人一区二区免费高清观看| 永久网站在线| 日韩 亚洲 欧美在线| 日韩av不卡免费在线播放| 一级黄片播放器| 日本与韩国留学比较| 91精品国产九色| 国内揄拍国产精品人妻在线| 丝袜喷水一区| 国产精品三级大全| 伦精品一区二区三区| 狠狠狠狠99中文字幕| 岛国毛片在线播放| 性色avwww在线观看| 永久网站在线| 午夜激情欧美在线| 亚洲精品日韩av片在线观看| 久久久久久久久久久丰满| 99久久中文字幕三级久久日本| 国产成人a区在线观看| 床上黄色一级片| 欧美潮喷喷水| 一级二级三级毛片免费看| 欧美人与善性xxx| 岛国在线免费视频观看| 九九在线视频观看精品| 亚洲国产精品成人久久小说| 只有这里有精品99| 成年av动漫网址| 日日撸夜夜添| 免费人成在线观看视频色| 九九热线精品视视频播放| 在线播放无遮挡| 精品免费久久久久久久清纯| 一级黄色大片毛片| 亚洲国产精品成人久久小说| 日本与韩国留学比较| 亚洲av不卡在线观看| 亚洲欧美成人综合另类久久久 | 激情 狠狠 欧美| 麻豆成人av视频| 日韩av在线大香蕉| 国产熟女欧美一区二区| 亚洲欧美中文字幕日韩二区| 亚洲精品日韩在线中文字幕| 老司机福利观看| 亚洲av男天堂| 国产伦精品一区二区三区四那| 91久久精品国产一区二区三区| 国产精品99久久久久久久久| av国产久精品久网站免费入址| 亚洲欧美精品自产自拍| 午夜激情福利司机影院| 久久精品国产自在天天线| 老师上课跳d突然被开到最大视频| 亚洲伊人久久精品综合 | 国产伦精品一区二区三区视频9| 丝袜喷水一区| 亚洲最大成人av| 亚洲在久久综合| 卡戴珊不雅视频在线播放| 全区人妻精品视频| 国产精品美女特级片免费视频播放器| 成年版毛片免费区| 亚洲欧美日韩卡通动漫| 亚洲国产高清在线一区二区三| 能在线免费观看的黄片| av国产免费在线观看| 色尼玛亚洲综合影院| 亚洲国产欧美在线一区| 日日摸夜夜添夜夜添av毛片| 性插视频无遮挡在线免费观看| 久久精品91蜜桃| 在线免费观看不下载黄p国产| av免费观看日本| 又爽又黄a免费视频| 国产黄a三级三级三级人| 亚洲成av人片在线播放无| 最近中文字幕高清免费大全6| 国产精品乱码一区二三区的特点| 日韩高清综合在线| 亚洲av中文av极速乱| 蜜桃亚洲精品一区二区三区| 久久久久久伊人网av| 青春草视频在线免费观看| 深爱激情五月婷婷| 三级男女做爰猛烈吃奶摸视频| 亚洲国产精品成人久久小说| 91av网一区二区| 精品久久久久久久久久久久久| 国产亚洲91精品色在线| 亚洲人成网站在线观看播放| 色播亚洲综合网| av在线蜜桃| 啦啦啦啦在线视频资源| 色吧在线观看| 日韩成人伦理影院| av国产久精品久网站免费入址| 永久网站在线| 又爽又黄无遮挡网站| 国产不卡一卡二| 级片在线观看| 久久久精品94久久精品| 黄色一级大片看看| 2021少妇久久久久久久久久久| 日本五十路高清| 直男gayav资源| 国产亚洲午夜精品一区二区久久 | 成人美女网站在线观看视频| 美女xxoo啪啪120秒动态图| 国产白丝娇喘喷水9色精品| 国产淫片久久久久久久久| 国产亚洲5aaaaa淫片| 九九爱精品视频在线观看| 国产精品人妻久久久影院| 精品久久久久久久人妻蜜臀av| 亚洲欧美日韩卡通动漫| 亚洲精品aⅴ在线观看| 国产精品久久久久久久久免| 在线免费观看的www视频| 日韩欧美在线乱码| 嫩草影院新地址| 国产午夜福利久久久久久| 少妇熟女欧美另类| 男女下面进入的视频免费午夜| 久久精品国产鲁丝片午夜精品| 国产男人的电影天堂91| 国产亚洲精品av在线| 午夜老司机福利剧场| 婷婷色麻豆天堂久久 | 国产精品人妻久久久影院| 国产成人一区二区在线| 好男人视频免费观看在线| 插逼视频在线观看| 最近2019中文字幕mv第一页| 日本wwww免费看| 最近最新中文字幕大全电影3| 青春草亚洲视频在线观看| 小说图片视频综合网站| 国产精品国产三级国产专区5o | 啦啦啦韩国在线观看视频| 午夜亚洲福利在线播放| 三级国产精品欧美在线观看| 成人二区视频| 亚洲精品乱久久久久久| 91狼人影院| 18禁裸乳无遮挡免费网站照片| 日本五十路高清| 老女人水多毛片| 亚洲av一区综合| 亚洲色图av天堂| 久久精品夜色国产| 亚洲av男天堂| 高清视频免费观看一区二区 | 老女人水多毛片| 听说在线观看完整版免费高清| 老司机影院毛片| 三级国产精品片| 七月丁香在线播放| 亚洲,欧美,日韩| 精品久久久久久久末码| 国产av在哪里看| 国产色爽女视频免费观看| 中文精品一卡2卡3卡4更新| 中国美白少妇内射xxxbb| 国产在视频线精品| 亚洲精品日韩av片在线观看| 亚洲av成人精品一区久久| 久久精品久久精品一区二区三区| 91久久精品电影网| 国产久久久一区二区三区| 色综合站精品国产| 99热6这里只有精品| 99久久中文字幕三级久久日本| 伦精品一区二区三区| 日韩亚洲欧美综合| 午夜a级毛片| 欧美高清成人免费视频www| 午夜免费激情av| 亚洲第一区二区三区不卡| 久久精品夜色国产| 免费电影在线观看免费观看| 精品少妇黑人巨大在线播放 | 中文欧美无线码| 亚洲在线自拍视频| 欧美zozozo另类| 亚洲av中文av极速乱| 老女人水多毛片| 免费观看性生交大片5| 日本免费一区二区三区高清不卡| 亚洲国产精品国产精品| 少妇裸体淫交视频免费看高清| 成人毛片60女人毛片免费| 亚洲精品乱码久久久v下载方式| 国产高清国产精品国产三级 | 女人被狂操c到高潮| 九色成人免费人妻av| 国产精品.久久久| 一级黄片播放器| 国产成年人精品一区二区| www.av在线官网国产| 一级黄片播放器| 国产一区亚洲一区在线观看| 女人久久www免费人成看片 | 色综合亚洲欧美另类图片| 欧美+日韩+精品| 乱系列少妇在线播放| av免费在线看不卡| 成人高潮视频无遮挡免费网站| 免费黄色在线免费观看| 亚州av有码| 亚洲欧美日韩东京热| 中文字幕精品亚洲无线码一区| 日韩三级伦理在线观看| 国产精品.久久久| 成年免费大片在线观看| 国产黄a三级三级三级人| 小说图片视频综合网站| 91精品国产九色| 久久久久久大精品| 亚洲中文字幕一区二区三区有码在线看| 18禁动态无遮挡网站| 青春草亚洲视频在线观看|