Endpoint results for weakly contractive mappings in $mathcal{F}$-metric spaces with application

Many researchers have provided certain interesting results for endpoints of some contractive multivalued mappings in metric spaces. In this paper, we introduce $alpha$-$zeta$-contractive multivalued mappings in $mathcal{F}$-metric spaces and establish some endpoint results in this framework. An illustrative example is given to elaborate the usability of our main result. In the sequel, we give some endpoint theorems for Suzuki-type contractive multivalued mappings and provide an application to integral equations.