On Multivalued Fuzzy Contractions in Extended b-Metric Spaces

Nayab Alamgir; Quanita Kiran; Hassen Aydi; Yaé Ulrich Gaba

doi:10.1155/2021/5579991

On Multivalued Fuzzy Contractions in Extended b-Metric Spaces

Nayab Alamgir
, Quanita Kiran
, Hassen Aydi^*
, Yaé Ulrich Gaba

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

In this paper, we establish a Hausdorff metric over the family of nonempty closed subsets of an extended b-metric space. Thereafter, we introduce the concept of multivalued fuzzy contraction mappings and prove related -fuzzy fixed point theorems in the context of extended b-metric spaces that generalize Nadler's fixed point theorem as well as many preexisting results in the literature. Further, we establish -fuzzy fixed point theorems for Círić type fuzzy contraction mappings as a generalization of previous results. Moreover, we give some examples to support the obtained results.

Original language	English
Article number	5579991
Journal	Journal of Mathematics
Volume	2021
DOIs	https://doi.org/10.1155/2021/5579991
Publication status	Published - 2021
Externally published	Yes

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abstract = "In this paper, we establish a Hausdorff metric over the family of nonempty closed subsets of an extended b-metric space. Thereafter, we introduce the concept of multivalued fuzzy contraction mappings and prove related -fuzzy fixed point theorems in the context of extended b-metric spaces that generalize Nadler's fixed point theorem as well as many preexisting results in the literature. Further, we establish -fuzzy fixed point theorems for C{\'i}ri{\'c} type fuzzy contraction mappings as a generalization of previous results. Moreover, we give some examples to support the obtained results.",

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AU - Gaba, Yaé Ulrich

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AB - In this paper, we establish a Hausdorff metric over the family of nonempty closed subsets of an extended b-metric space. Thereafter, we introduce the concept of multivalued fuzzy contraction mappings and prove related -fuzzy fixed point theorems in the context of extended b-metric spaces that generalize Nadler's fixed point theorem as well as many preexisting results in the literature. Further, we establish -fuzzy fixed point theorems for Círić type fuzzy contraction mappings as a generalization of previous results. Moreover, we give some examples to support the obtained results.

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On Multivalued Fuzzy Contractions in Extended b-Metric Spaces

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