On the multivalued $ \rho _{\ast } $-interpolative contractions in fuzzy metric spaces with application to nonlinear matrix equations

In this study, the subject of the multivalued $ \rho _{\ast } $-interpolative Ćirić-Reich-Rus-type fuzzy contractions is introduced and investigated in which the $ \vartheta $-comparison functions and the property of the $ \rho _{\ast } $-admissibility play an important role. In the first step, the existence of fixed point theorems is proven for such a type of contractions in the context of the complete fuzzy metric spaces. Then, some of the results are extended in the framework of the fuzzy metric spaces equipped with a partial order. In this direction, we give some examples to clarify the obtained results and definitions. Additionally, we demonstrate an application about the solutions of non-linear matrix equations on the basis of fixed points of these new contractions.