Fixed point results of fuzzy mappings with applications

Abstract

<abstract><p>Jleli and Samet introduced the notion of $ \mathcal{F} $-metric space as a generalization of traditional metric space and proved Banach contraction principle in the setting of these generalized metric spaces. The aim of this article is to utilize $ \mathcal{F} $-metric space and establish some common $ \alpha $-fuzzy fixed point theorems for rational ($ \beta $-$ \phi) $-contractive conditions. Our results extend, generalize and unify some well-known results in the literature. As application of our main result, we discuss the solution of fuzzy integrodifferential equations in the setting of a generalized Hukuhara derivative.</p></abstract>