概率内积空间中映象的不动点定理
Fixed Point Theorem in Probabilistic Inner Product Spaces
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摘要: 本文的目的一是对概率度量空间引入一修正的定义;二是对这一空间中的映象建立了几个新的不动点定理.作为本文结果的应用,我们在第四节中讨论了L2(G)空间中Uryson算子方程解的存在性和唯一性问题.Abstract: The purpose of this paper is to introduce a new maditying detinition for probabilistie inner product space, and to establish seveeral new fixed point theorems for mappings on such kind of spaces. As an example of applications, we utilize the results of this paper to study the existence and uniqueness of solution of Urysons integral equation in [4].
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[1] Schweizer.B.and A.Sklar.Probahilistic Metric Spaces,North-Holland.New York.Amsterdam,Oxford.(1982). [2] Dumitrescu,C.,Un Produit scalaire probabiliste.Rev.,Roum.Math.Pureet Appl.,26.3(1981).399-404. [3] Krasnoselskii.M,A.,Topological Methods in the Theory of Nonlinear Integral Equations,Pergamon Press.Oxford,London.New York.Paris.(1964). -
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