一般随机不动点定理及其应用
General Random Fixed Point Theorem and Its Applications
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摘要: 在本文中我们得到了一个一般的随机不动点定理,推广了Engl[4,7]和Bocsan[8]的主要结果.这一定理的有用性在于目前由许多作者用特殊方法得到的随机不动点定理[1,4,5-13]均能利用我们的一般定理(定理1和系1,2)得到,最后给出了我们的定理对随机积分和微分方程的应用.Abstract: 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.
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[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
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