Generalized contraction mapping principles in probabilistic metric spaces

O. Hadžić, E. Pap, V. Radu

Research output: Contribution to journalArticle

35 Citations (Scopus)

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, script F sign, T), where T belongs to a more general class of continuous t-norms than in the previous case where T = TM (= 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, script K sign, P) is given.

Original languageEnglish
Pages (from-to)131-148
Number of pages18
JournalActa Mathematica Hungarica
Volume101
Issue number1-2
DOIs
Publication statusPublished - Oct 2003

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Keywords

  • Admissible subset
  • Fixed point
  • Generalized probabilistic contraction mapping
  • Probabilistic metric space
  • Random normed space
  • Triangular norm

ASJC Scopus subject areas

  • Mathematics(all)

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