@misc{10498/40378,
year = {2025},
month = {2},
url = {http://hdl.handle.net/10498/40378},
abstract = {In this work we extend concepts of differentiability for Interval-Valued functions (IVfunctions)
of multiple variables, based on generalized Hukuhara gH-difference. In this
context, we introduce a new concept of gH-linearity and characterize the class of gHlinear
IV-functions, which are fundamental for a general approach to Fréchet-type and
Gateaux-type gH-differentiability of the first order. We moreover consider vector IVfunctions
and outline the definition of the gH-Jacobian; by representing intervals and
IV-functions in midpoint-radius notation, we establish properties and relations between
pointwise, Fréchet and Gateaux gH-differentiability. Finally, higher-order differentiability
and gH-Hessian matrix are considered. These intuitive concepts are mathematically
and computationally easy to work with.},
publisher = {Elsevier},
keywords = {Interval Valued Functions},
keywords = {gH-linearity},
keywords = {Fréchet gH-differentiability},
keywords = {Gateaux interval derivative},
keywords = {Interval gradient},
keywords = {Interval Jacobian and Hessian matrices},
title = {Fréchet and Gateaux gH-differentiability for interval valued functions of multiple variables},
doi = {https://doi.org/10.1016/j.ins.2024.121601},
author = {Stefanini, Luciano and Arana Jiménez, Manuel and Sorini, Laerte},
}