Fuzzy fixed point results for $ \alpha $-admissible $ \phi $-$ \psi $-set-valued fuzzy contractions

Shazia Kanwal; Rehmatullah Madni; Hassen Aydi; Sami Baraket; Shazia Kanwal; Rehmatullah Madni; Hassen Aydi; Sami Baraket

doi:10.3934/math.2026404

AIMS Mathematics

2026, Volume 11, Issue 4: 9760-9787. doi: 10.3934/math.2026404

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Research article

Fuzzy fixed point results for $ \alpha $-admissible $ \phi $-$ \psi $-set-valued fuzzy contractions

1.
Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
2.
Université de Sousse, Institut Supérieur d'Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia
3.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health University, Ga-Rankuwa, South Africa
4.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi Arabia

Received: 22 January 2026 Revised: 26 March 2026 Accepted: 30 March 2026 Published: 13 April 2026
MSC : 46S40, 54H25, 47H10, 37C25, 47H09

Fixed point theory and fuzzy mathematics offer powerful tools for addressing real-world problems involving uncertainty and imprecision. In this paper, we introduced a generalized framework for $ \alpha- $admissible fuzzy set-valued contractive mappings by extending the existing concepts of $ \phi $-set-valued and $ \phi $-$ \psi $-set-valued contractions in the setting of $ b $-metric spaces. We established several fixed point theorems under these generalized contractive conditions, thereby extending and enriching the existing theory. As an additional contribution, we also explored fixed point results under Kannan-type and Reich-type conditions within the same framework. Notably, several classical fixed point results were recovered as special cases of our findings, demonstrating the unifying nature of our approach. To illustrate the applicability and non-triviality of the results, a concrete example was provided.
- admissible mapping,
- fixed point,
- fuzzy fixed point,
- $ \phi $-$ \psi $-set-valued contraction,
- $ b $-metric space
Citation: Shazia Kanwal, Rehmatullah Madni, Hassen Aydi, Sami Baraket. Fuzzy fixed point results for $ \alpha $-admissible $ \phi $-$ \psi $-set-valued fuzzy contractions[J]. AIMS Mathematics, 2026, 11(4): 9760-9787. doi: 10.3934/math.2026404

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Abstract

Fixed point theory and fuzzy mathematics offer powerful tools for addressing real-world problems involving uncertainty and imprecision. In this paper, we introduced a generalized framework for $ \alpha- $admissible fuzzy set-valued contractive mappings by extending the existing concepts of $ \phi $-set-valued and $ \phi $-$ \psi $-set-valued contractions in the setting of $ b $-metric spaces. We established several fixed point theorems under these generalized contractive conditions, thereby extending and enriching the existing theory. As an additional contribution, we also explored fixed point results under Kannan-type and Reich-type conditions within the same framework. Notably, several classical fixed point results were recovered as special cases of our findings, demonstrating the unifying nature of our approach. To illustrate the applicability and non-triviality of the results, a concrete example was provided.

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