We establish common fixed point theorems for fuzzy mappings under a $\varphi$-contraction condition on a metric space with the d_$\infty$-metric (induced by the Hausdorff metric) on the family of fuzzy sets. The study of fixed points of fuzzy set-valued mappings related to the d_$\infty$-metric is useful in geometric problems arising in high energy physics. Our results generalize some recent results.
Azam, A., Arshad, M., Vetro, P. (2010). On a pair of fuzzy $\varphi$-contractive mappings. MATHEMATICAL AND COMPUTER MODELLING, 52(1-2), 207-214 [10.1016/j.mcm.2010.02.010].
On a pair of fuzzy $\varphi$-contractive mappings
VETRO, Pasquale
2010-01-01
Abstract
We establish common fixed point theorems for fuzzy mappings under a $\varphi$-contraction condition on a metric space with the d_$\infty$-metric (induced by the Hausdorff metric) on the family of fuzzy sets. The study of fixed points of fuzzy set-valued mappings related to the d_$\infty$-metric is useful in geometric problems arising in high energy physics. Our results generalize some recent results.
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