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Probabilistic B-contraction principles for single-valued mappings

  • Olga Hadžić
  • Endre Pap
Chapter
  • 444 Downloads
Part of the Mathematics and Its Applications book series (MAIA, volume 536)

Abstract

The first fixed point theorem in probabilistic metric spaces was proved by Sehgal and Barucha-Reid [272] for mappings f : SS, where (S, F, T M) is a Menger space. Further development of the fixed point theory in a more general Menger space (S, F, T) was connected with investigations of the structure of the t-norm T. Very soon the problem was in some sense completely solved. Namely, if we restrict ourselves to complete Menger spaces (S, F, T), where T is a continuous t-norm, then any probabilistic q-contraction f : SS has a fixed point if and only if the t-norm is of H-type.

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Olga Hadžić
    • 1
  • Endre Pap
    • 1
  1. 1.Institute of MathematicsUniversity of Novi SadYugoslavia

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