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随机定向收缩及其应用*

丁协平

丁协平. 随机定向收缩及其应用*[J]. 应用数学和力学, 1986, 7(12): 1107-1120.
引用本文: 丁协平. 随机定向收缩及其应用*[J]. 应用数学和力学, 1986, 7(12): 1107-1120.
Ding Xie-ping. Random Directional Contractors and Their Applications[J]. Applied Mathematics and Mechanics, 1986, 7(12): 1107-1120.
Citation: Ding Xie-ping. Random Directional Contractors and Their Applications[J]. Applied Mathematics and Mechanics, 1986, 7(12): 1107-1120.

随机定向收缩及其应用*

基金项目: * 中国科学院科学基金资助的课题

Random Directional Contractors and Their Applications

  • 摘要: 作为Altman的定向收缩理论[4,5]和Lee,Padgett的随机收缩理论[1,2]的推广,本文对非线性集值随机算子引入了随机定向收缩概念,利用这一新概念和超限归纳法,我们证明了非线性集值随机算子方程随机解的几个存在性定理.这些定理分别改进和推广了[1,2,4,5,11]中相应的结果.其次,给出了我们的结果对非线性随机积分和微分方程的某些应用.
  • [1] Lee,A.C.H.and W.J.Padgett,Random contractors and the solution of random nonlinear equation,Nonlinear Anal.TMA,1(1977),175-185.
    [2] Lee,A.C.H.and W.J.Padgett,Random Contractors with random nonlinear majorant functions,Nonlinear Anal.TMA,3(1979),707-715.
    [3] Lee,A.C.H.and W.J.Padgett,Solution of random operator equations by random stepcontractors,Nonlinear Anal.TMA,4(1980),145-151.
    [4] Altman,M.,Contractor directions,directional contractors and directional contractions for solving equations,Pacific J.Math.,62(1976),1-18.
    [5] Altman,M.,Contractors and Contractors Directions-Theory and Applications,Maroel Dekker(1977).
    [6] Bharucha-Reid,A.T.,Random Integral Equations,Acad.Press,New York(1974).
    [7] Tsokos,C.P.and W.J.Padgett,Random Integral Equations.with Applications in Life Sciences and Engineering,Acad Press,New York(1974).
    [8] Ding Xie-ping,Existence,uniqueness and approximation of solutions for a system of nonlinear random operator equations,Nonlinear Anal.TMA,8,6(1984),563-576.
    [9] 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),561-575
    [10] Castaing,C.and M.Valadier,Convex Analysis and Measurable Multi functions,Springer-Verlag(1977),580.
    [11] Itoh,S.,A random fixed point theorem for a multivalued contraction mapping,Pacific J.Math.,68(1977),85-90.
    [12] 丁协平,随机收缩和随机算子方程的解,数学学报,29,1(1986),135-144
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出版历程
  • 收稿日期:  1984-10-03
  • 刊出日期:  1986-12-15

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