Ding Xie-ping. General Random Fixed Point Theorem and Its Applications[J]. Applied Mathematics and Mechanics, 1984, 5(5): 699-708.
Citation: Ding Xie-ping. General Random Fixed Point Theorem and Its Applications[J]. Applied Mathematics and Mechanics, 1984, 5(5): 699-708.

General Random Fixed Point Theorem and Its Applications

  • Received Date: 1983-08-12
  • Publish Date: 1984-10-15
  • In this paper,we obtain a general random fixed point theorem which generalizes the main results of Engle[4,7] and Bocsan[8]. The usefulness of this theorem seems to lie in the fact that unlike many random fixed point theorems obtained by using special methods[1,4,5-13] can be proved by using out general theorem(Theorem 1 and Corollaries 1 and 2). Finally,we indicate some possible applications of our results to nonlinear random integral and differential equations.
  • loading
  • [1]
    Bharucha-Reid,A.T.,Random Integral Equations,Acad.Press,New York,(1972).
    [2]
    Tsokos,C.P.and W.J.Padgett,Random Integral Equations,with Applications to Life Sciences and Engineering,Acad.Press,New York,(1974).
    [3]
    Morse,W.L.The dishonest method in stream temperature modeling,Water Resour.Res.,14(1978),45-51.
    [4]
    Engl.H.W.,A general stochastic fixed point theorem for continuous random operators on stochastic domains,J.Math.Anal.Appl.,66(1978),220-231.
    [5]
    Bharugha-Reid,A.T.,Fixed point theorems in probabilistic analysis,Bull.Amer.Math.Soc.,82(1976),641-657.
    [6]
    王梓坤,随机泛函分析引论,数学进展,5(1962),45-71
    [7]
    Engl,H.W.,Random fixed point theorems,in Nonlinear Equations in Abstract Spaces,Acad.Press,New York,(1978),67-80.
    [8]
    Bocsan,Gh.,A general random fixed point theorem and applications to random equation,Rev.Roum.Math.Pures et Appl.,26(1981),381-384.
    [9]
    Iton,S.,A random fixed point theorem for a multivalued contraction mapping,Pacific J.Math.,68(1977),85-90.
    [10]
    丁协平,连续随机算子的不动点定理,数学进展,12(1983),294-298.
    [11]
    刘作述、陈绍仲,随机集值映象的不动点定理,科学通报,27(1982),1161-1162.
    [12]
    张石生、陈绍仲,概率分析中的随机不动点定理及其对随机逼近论的应用,应用数学学报,5(1982),300-309.
    [13]
    Chang,S.S.,Random fixed point theorem in probabilistic analysis,Nonlinear Anal.,5(1981),113-122.
    [14]
    Mimmeberg,C.J.,Measurable relations,Fund.Math.,87(1975),53-72.
    [15]
    Castaing,C.and M.Valadier,Convex Analysis and Measurable Multifunctions,Springer-Verlag,(1977),580.
    [16]
    Himmeberg,C.J.and F.S.Van Vleck,Multifunctions on abstract measurable spaces and application to stochastic decision theory,Annali di Mat.Pura ed Appl.,101(1974),229-236.
    [17]
    丁协平.集值压缩型映象的公共不动点定理,四川师院学抵数学专辑(1981),26-34.
    [18]
    丁协平,非扩展型映射的某些不动点定理,数学进展,12(1983).133-140.
    [19]
    丁协平.集值非自映射的某些不动点定理,数学研究与评论,(将发表).
    [20]
    Assad,N.A.and W.A.Kirk,Fixed point theorems for set-valued mappings of contractive type,Pacific J.Math.,43(1972),553-562.
    [21]
    Khan,M.S.,Common fixed point theorems for multivalued mappings,Pacific J.Math.,95(1981),337-347.
    [22]
    丁协平,某些压缩映象的不动点定理及其相互关系,数学学报,(待发表).
    [23]
    丁协平,轨道压缩映射的不动点定理,数学年刊,2(1981),511-517.
    [24]
    Ding Xie-ping,Fixed point theorems of gneeralized contractive type mappings(Ⅱ),Chin.Ann.of Math.,4B(1983),153-163.
    [25]
    Roseau.M(叶彦谦译),《常微分方程》,上海科技出版社(1981).
    [26]
    丁协平,随机集值映射的不动点定理及其应用,应用数学和力学,5,4(1984).
    [27]
    丁协平.关于抽象非线性Volterra积分方程解的存在唯一性定理,数学汇刊.3(1982).56-61
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1714) PDF downloads(660) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return