{"ID":2872970,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.07565","arxiv_id":"2509.07565","title":"On the Characterization of gH-partial derivatives and gH-Product for Interval-Valued Functions","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.","short_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 in...","url_abs":"https://arxiv.org/abs/2509.07565","url_pdf":"https://arxiv.org/pdf/2509.07565v1","authors":"[\"Amir Suhail\",\"Tauheed\",\"Akhlad Iqbal\"]","published":"2025-09-09T10:07:07Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}