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

Olga Hadžić, E. Pap, Mirko Budinčević

Research output: Contribution to journalArticle

58 Citations (Scopus)

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 ≥ 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.

Original languageEnglish
Pages (from-to)363-382
Number of pages20
JournalKybernetika
Volume38
Issue number3
Publication statusPublished - 2002

Fingerprint

Menger Space
Probabilistic Metric Space
Triangular Norm
Fixed Point Theory
T-norm
Fixed point theorem
Countable
Random Operators
Operator Equation
Contraction
Family

ASJC Scopus subject areas

  • Human-Computer Interaction
  • Control and Systems Engineering

Cite this

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

In: Kybernetika, Vol. 38, No. 3, 2002, p. 363-382.

Research output: Contribution to journalArticle

@article{204d8494d533422da1b110189af36108,
title = "Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces",
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 ≥ 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, Acz{\'e}l-Alsina, and Sugeno-Weber families of t-norms. An application to random operator equations is obtained.",
author = "Olga Hadžić and E. Pap and Mirko Budinčević",
year = "2002",
language = "English",
volume = "38",
pages = "363--382",
journal = "Kybernetika",
issn = "0023-5954",
publisher = "Academy of Sciences of the Czech Republic",
number = "3",

}

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 -