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Applied Mathematics and Mechanics (English Edition) ›› 2007, Vol. 28 ›› Issue (6): 799-809 .doi: https://doi.org/10.1007/s10483-007-0610-z

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Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations

  

  • 收稿日期:2006-07-10 修回日期:2007-01-31 出版日期:2007-06-18 发布日期:2007-06-18

Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations

Servet Kutukcu, Adnan Tuna, Atakan T. Yakut   

    1. Department of Mathematics, Faculty of Science and Arts, Ondokuz Mayis University, Kurupelit, 55139 Samsun, Turkey;
    2. Department of Mathematics, Faculty of Science and Arts, Gazi University, Teknikokullar, 06500 Ankara, Turkey;
    3. Department of Mathematics, Faculty of Science and Arts, Nigde University, Nigde, Turkey
  • Received:2006-07-10 Revised:2007-01-31 Online:2007-06-18 Published:2007-06-18
  • Contact: Servet Kutukcu

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Abstract: Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.

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