On the Characterization of gH-partial derivatives and gH-Product for Interval-Valued Functions
Optimization and Control
2025-09-10 v1
Abstract
In this paper, we show by a counterexample that the gH-partial derivative of interval-valued functions (IVFs) may exist even when the partial derivative of the end point functions do not. Next, we introduce the gH-partial derivative in terms of gH-derivative and discuss its complete characterization. Furthermore, we introduce the gH-product of a vector with an n-tuples of intervals and illustrate by a suitable example that our definition refines the definition existing in the literature. To illustrate and validate these definitions, we provide several non-trivial examples.
Cite
@article{arxiv.2509.07565,
title = {On the Characterization of gH-partial derivatives and gH-Product for Interval-Valued Functions},
author = {Amir Suhail and Tauheed and Akhlad Iqbal},
journal= {arXiv preprint arXiv:2509.07565},
year = {2025}
}