概率度量空间的基本理论及应用(Ⅱ)*
Basic Theory and Applications of Probabilistic Metric Spaces(Ⅱ)
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摘要: 本文是作者文章[1]的继续.得出了概率度量空间的集合的各种概率有界性的表征.借助于这些结果及[1]中所得结果,讨论了概率线性赋范空间中的线性算子理论及概率度量空间映象的不动点定理.Abstract: This paper is a continuation of the author's previous paper [1],in which the characterizations of various probabilistically bounded sets are presented,and the linear operator theory and fixed point theory on probabilistic metric spaces are given,too.
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[1] 张石生,概率度量空间的基本理论(Ⅰ),应用数学和力学,9,2(1988). [2] 张石生,《不动点理论及应用》,重庆出版社(1984). [3] Zhang Shi-sheng,The metrization of probabilistic metric spaces with applications,Zbornike radova Prirodno-matematickog fakulteta,u Novom Sadu,Serija za matematiku,15,1(1985),107-117. [4] Hadžič,O.,Some fixed point theorems in probabilistic metric space,Ibid.15 1(1985),23-36. [5] Zhang Shi-sheng,On the theory of probabilistic metric spaces with applications,Z.Wahrscheinlichkeitstheorie vcrw.Gebiete,67(1984),85-94. [6] 张石生,PM-空间与映象的不动点定理,数学研究与评,5,3(1985),23-28 [7] Constantin,Gh.,On some classes of contraction mappings in Menger spaces,Seminarul de Teoria Probubilitatilor si Applicatii,76(1985),1-10. [8] Radu,V.,On some fixed point theorems in probabilistic metric spaces.1bid.,74(1985),1-10. [9] Nadler,S.B.,Multi-valued contraction mappings,Pacific J.Math.,30(1969),475-487. [10] 游兆永等,论概率赋范空间上的线性算子及其它,全国第四次泛函分析会议论文资料(1986). [11] 张文修、张继国,PM-空间中概率直径的特征及LPM-空间,工程数学学报,2(1985).
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