A new type of fixed point theorem via interpolation of operators with application in homotopy theory

The purpose of this paper is to introduce the class of multi-valued operators by the technique of interpolation of operators. Our results extend and generalize several results from the existing literature. Moreover, we also study the data dependence problem of the fixed point set and Ulam–Hyers stability of the fixed point problem for the operators introduced herein. Moreover, as an application, we obtain a homotopy result.