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Generalized contraction mapping principles in probabilistic metric spaces

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Abstract

We give an improvement of Theorem 1 from [2] with a quite different approach, which enable us to prove that the fixed point is also globally attractive. In Theorem 2.11 a further generalization is obtained for a complete Menger space (S,F,T), where T belongs to a more general class of continuous t-norms than in the previous case where T=T M (=min). Theorem 3.2 is a generalization of Theorem 2 from [2]. Thereafter the notion of a generalized C-contraction of Krasnoselski's type is introduced and a fixed point theorem for such mappings is proved. An application in the space S(Ω, K, P) is given.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, University of Novi Sad, Trg D. Obradovića 4, 21000, Novi Sad, Serbia and Montenegro

    O. Hadžić & E. Pap

  2. Faculty of Mathematics, West University of Timisoara Bv. Vasile Parvan 4, 1900, Timisoara, Romania

    V. Radu

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  1. O. Hadžić
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  2. E. Pap
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  3. V. Radu
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Hadžić, O., Pap, E. & Radu, V. Generalized contraction mapping principles in probabilistic metric spaces. Acta Mathematica Hungarica 101, 131–148 (2003). https://doi.org/10.1023/B:AMHU.0000003897.39440.d8

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