Some notes on the switching points for the generalized Hukuhara differentiability of interval-valued functions

Abstract

In this paper, we give some comments on the recent results about the switching points for the gH-differentiability of interval-valued functions. We show by counterexamples that there exist switching points which are not critical points of the length function, and that there are GH-differentiable functions with an infinite number of switching points and gH-differentiable functions with an uncountable number of switching points. After reclassifying the switching points more finely, we also present some characterizations for the switching points. The obtained results correct the known ones in the literature.