The generalized Hukuhara differentiability of interval-valued function is not fully equivalent to the one-sided differentiability of its endpoint functions

In this paper, we first show by a counterexample that the generalized Hukuhara differentiability of interval-valued function at a point is not fully equivalent to the one-sided differentiability of its endpoint functions, then present a complete characterization of the generalized Hukuhara differentiability of interval-valued functions. The obtained results include the existing cases in the literature and the new cases that correspond to the rather odd scenario of functions being gH-differentiable at a point, but not continuous in any deleted neighborhood of that point.& nbsp; (c) 2020 Elsevier B.V. All rights reserved.

Automated summary

The paper demonstrates that the generalized Hukuhara differentiability of interval-valued function at a point is not fully equivalent to the one-sided differentiability of its endpoint functions through a counterexample, and then presents a complete characterization of the generalized Hukuhara differentiability of interval-valued functions. The results include existing cases in the literature and new cases where functions are gH-differentiable at a point but not continuous in any deleted neighborhood of that point.