### Abstract

In this paper a fixed point theorem for a probabilistic q-contraction f : S → S, where (S, F, T) is a complete Menger space, F satisfies a grow condition, and T is a g-convergent t-norm (not necessarily T ≥ T_{L}) is proved. There is proved also a second fixed point theorem for mappings f : S → S, where (S, F, T) is a complete Menger space, T satisfy a weaker condition than in [13], and T belongs to some subclasses of Dombi, Aczél-Alsina, and Sugeno-Weber families of t-norms. An application to random operator equations is obtained.

Original language | English |
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Pages (from-to) | 363-382 |

Number of pages | 20 |

Journal | Kybernetika |

Volume | 38 |

Issue number | 3 |

Publication status | Published - 2002 |

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### ASJC Scopus subject areas

- Human-Computer Interaction
- Control and Systems Engineering

### Cite this

*Kybernetika*,

*38*(3), 363-382.

**Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces.** / Hadžić, Olga; Pap, E.; Budinčević, Mirko.

Research output: Contribution to journal › Article

*Kybernetika*, vol. 38, no. 3, pp. 363-382.

}

TY - JOUR

T1 - Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces

AU - Hadžić, Olga

AU - Pap, E.

AU - Budinčević, Mirko

PY - 2002

Y1 - 2002

N2 - In this paper a fixed point theorem for a probabilistic q-contraction f : S → S, where (S, F, T) is a complete Menger space, F satisfies a grow condition, and T is a g-convergent t-norm (not necessarily T ≥ TL) is proved. There is proved also a second fixed point theorem for mappings f : S → S, where (S, F, T) is a complete Menger space, T satisfy a weaker condition than in [13], and T belongs to some subclasses of Dombi, Aczél-Alsina, and Sugeno-Weber families of t-norms. An application to random operator equations is obtained.

AB - In this paper a fixed point theorem for a probabilistic q-contraction f : S → S, where (S, F, T) is a complete Menger space, F satisfies a grow condition, and T is a g-convergent t-norm (not necessarily T ≥ TL) is proved. There is proved also a second fixed point theorem for mappings f : S → S, where (S, F, T) is a complete Menger space, T satisfy a weaker condition than in [13], and T belongs to some subclasses of Dombi, Aczél-Alsina, and Sugeno-Weber families of t-norms. An application to random operator equations is obtained.

UR - http://www.scopus.com/inward/record.url?scp=0036978909&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036978909&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0036978909

VL - 38

SP - 363

EP - 382

JO - Kybernetika

JF - Kybernetika

SN - 0023-5954

IS - 3

ER -