On Fixed Point for Derivative of Set-Valued Functions

Abstract

In this article, we showed the existence of a fixed point for the derivative of interval-valued functions. The investigation of the existence of such fixed points utilizes the common fixed point concepts for two mappings. Under the condition of compatibility of the hybrid composite mappings in the sense of the Pompei-Hausdorff metric the existence of a fixed point for the derivative is shown. Some examples to support the usability of the result of this study are also given.