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直觉Menger空间中的广义压缩映射原理及其在微分方程中的应用

S·库图苏 A·图纳 A·T·雅库特

S·库图苏, A·图纳, A·T·雅库特. 直觉Menger空间中的广义压缩映射原理及其在微分方程中的应用[J]. 应用数学和力学, 2007, 28(6): 713-723.
引用本文: S·库图苏, A·图纳, A·T·雅库特. 直觉Menger空间中的广义压缩映射原理及其在微分方程中的应用[J]. 应用数学和力学, 2007, 28(6): 713-723.
Servet Kutukcu, Adnan Tuna, Atakan T. Yakut. Generalized Contraction Mapping Principle in Intuitionistic Menger Spaces and an Application to Differential Equations[J]. Applied Mathematics and Mechanics, 2007, 28(6): 713-723.
Citation: Servet Kutukcu, Adnan Tuna, Atakan T. Yakut. Generalized Contraction Mapping Principle in Intuitionistic Menger Spaces and an Application to Differential Equations[J]. Applied Mathematics and Mechanics, 2007, 28(6): 713-723.

直觉Menger空间中的广义压缩映射原理及其在微分方程中的应用

详细信息
  • 中图分类号: O177.3;175.15;189.2

Generalized Contraction Mapping Principle in Intuitionistic Menger Spaces and an Application to Differential Equations

  • 摘要: 利用Atanassov的思路,将直觉Menger空间定义为由Menger提出的Menger空间的自然推广.同时也得出一个新广义压缩映射,并运用该压缩映射证明了直觉Menger空间中微分方程解的存在性定理.
  • [1] Menger K. Statistical metric spaces[J].Proc Nat Acad Sci,1942,28:535-537. doi: 10.1073/pnas.28.12.535
    [2] Schweizer B,Sklar A. Statistical metric spaces[J].Pacific J Math,1960,10(1):313-334.
    [3] Schweizer B,Sklar A.Probabilistic Metric Spaces[M].New York:North-Holland,1983.
    [4] Schweizer B, Sklar A,Thorp E. The metrization of statistical metric spaces[J].Pacific J Math,1960,10:673-675.
    [5] Chang S S, Lee B S,Cho Y J,et al.Generalized contraction mapping principle and differential equations in probabilistic metric spaces[J].Proceedings of the American Mathematical Society,1996,124(8):2367-2376. doi: 10.1090/S0002-9939-96-03289-3
    [6] Hadzic O,Pap E.Fixed Point Theory in Probabilistic Metric Spaces[M].Dordrecht:Kluwer Acad Pub,2001.
    [7] Hadzic O, Pap E,Radu V. Generalized contraction mapping principles in probabilistic metric spaces[J].Acta Math Hungar,2003,101(1/2):131-148.
    [8] Mihet D. On the contraction principle in Menger and non-Archimedean Menger spaces[J].An Univ Timisoara Ser Mat Inform,1994,32(2):45-50.
    [9] Klement E P, Mesiar R,Pap E.Triangular Norms[M].Trends in Logic 8.Dordrecht:Kluwer Acad Pub,2000.
    [10] Radu V.Lectures on Probabilistic Analysis[M].West University of Timisoara, 1996.
    [11] Radu V. Some remarks on the probabilistic contractions on fuzzy Menger spaces[A/J]. In:The Eighth Internat Conf on Applied Mathematics and Computer Science[C].Cluj-Napoca, 2002;Automat Comput Appl Math,2002,11(1):125-131.
    [12] Kramosil O,Michalek J. Fuzzy metric and statistical metric spaces[J].Kybernetica,1975,11:326-334.
    [13] George A,Veeramani P. On some results in fuzzy metric spaces[J].Fuzzy Sets and Systems,1994,64:395-399. doi: 10.1016/0165-0114(94)90162-7
    [14] Mihet D. A Banach contraction theorem in fuzzy metric spaces[J].Fuzzy Sets and Systems,2004,144:431-439. doi: 10.1016/S0165-0114(03)00305-1
    [15] Park J H. Intuitionistic fuzzy metric spaces[J].Chaos, Solitons & Fractals,2004, 22:1039-1046.
    [16] Kelley J L.General Topology[M].Princeton, 1955.
    [17] Atanassov K.Intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1986,20:87-96. doi: 10.1016/S0165-0114(86)80034-3
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出版历程
  • 收稿日期:  2006-07-10
  • 修回日期:  2007-02-01
  • 刊出日期:  2007-06-15

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