Ćirić type nonunique fixed point theorems in the frame of fuzzy metric spaces

Tatjana Došenović; Dušan Rakić; Stojan Radenović; Biljana Carić; Tatjana Došenović; Dušan Rakić; Stojan Radenović; Biljana Carić

doi:10.3934/math.2023111

AIMS Mathematics

2023, Volume 8, Issue 1: 2154-2167. doi: 10.3934/math.2023111

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Ćirić type nonunique fixed point theorems in the frame of fuzzy metric spaces

1.
Faculty of Technology Novi Sad, Bulevar cara Lazara 1, University of Novi Sad, Serbia
2.
Faculty of Mechanical Engineering, University of Belgrade, Serbia
3.
Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, University Novi Sad, Serbia

Received: 24 August 2022 Revised: 12 September 2022 Accepted: 13 September 2022 Published: 28 October 2022
MSC : 47H10, 54H25

The paper defines a new contractive condition within $ \kappa- $orbitally complete fuzzy metric spaces $ (\Theta, \mathcal{M}, \mathcal{T}) $, as well as fixed point theorems for single-valued and multi-valued function on $ \Theta $ which is not necessarily continuous. The contractive condition is motivated by an idea proposed in Ćirić's paper "On some maps with a nonunique fixed points". Continuity of mapping $ \kappa $ is replaced by $ \kappa- $orbitally continuity property which provides the existence of the fixed point, but not necessarily uniqueness.
- fixed point,
- fuzzy metric space,
- $ t $-norm,
- ćiric type contraction,
- Cauchy sequence
Citation: Tatjana Došenović, Dušan Rakić, Stojan Radenović, Biljana Carić. Ćirić type nonunique fixed point theorems in the frame of fuzzy metric spaces[J]. AIMS Mathematics, 2023, 8(1): 2154-2167. doi: 10.3934/math.2023111

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Abstract

The paper defines a new contractive condition within $ \kappa- $orbitally complete fuzzy metric spaces $ (\Theta, \mathcal{M}, \mathcal{T}) $, as well as fixed point theorems for single-valued and multi-valued function on $ \Theta $ which is not necessarily continuous. The contractive condition is motivated by an idea proposed in Ćirić's paper "On some maps with a nonunique fixed points". Continuity of mapping $ \kappa $ is replaced by $ \kappa- $orbitally continuity property which provides the existence of the fixed point, but not necessarily uniqueness.

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