Best proximity point theorems for interpolative Kannan-type and Ćirić–Reich–Rus-type $\mathcal{L} $-proximal contractions

In this paper, we introduce several different types of interpolative proximal contractions in complete fuzzy metric spaces. We establish some best proximity point results for Kannan-type and Ćirić–Reich–Rus-type $\mathcal{L} $ -proximal contractions in complete fuzzy metric spaces. The obtained results can be applied to the solution of entity uniqueness problems, which arise in many fields, especially in the applied field. As an application, we present the existence of solutions of entity uniqueness problems.