Some fixed points of multivalued maps in multiplicative metric spaces

In this manuscript, new fixed point theorems for multivalued maps, particularly $\alpha -\varphi$ contractions, in complete multiplicative metric spaces are proved. We further prove a fixed point theorem for multivalued mappings on a graph-equipped multiplicative metric space. Our results extend the result of Dosenovic et al. [4], and generalize the result of Ali et al. [2]. We included an example to validate our result.