RT journal article
T1 Fréchet and Gateaux gH-differentiability for interval valued functions of multiple variables
A1 Stefanini, Luciano
A1 Arana Jiménez, Manuel
A1 Sorini, Laerte
A2 Estadística e Investigación Operativa
K1 Interval Valued Functions
K1 gH-linearity
K1 Fréchet gH-differentiability
K1 Gateaux interval derivative
K1 Interval gradient
K1 Interval Jacobian and Hessian matrices
AB In this work we extend concepts of differentiability for Interval-Valued functions (IVfunctions)of multiple variables, based on generalized Hukuhara gH-difference. In thiscontext, we introduce a new concept of gH-linearity and characterize the class of gHlinearIV-functions, which are fundamental for a general approach to Fréchet-type andGateaux-type gH-differentiability of the first order. We moreover consider vector IVfunctionsand outline the definition of the gH-Jacobian; by representing intervals andIV-functions in midpoint-radius notation, we establish properties and relations betweenpointwise, Fréchet and Gateaux gH-differentiability. Finally, higher-order differentiabilityand gH-Hessian matrix are considered. These intuitive concepts are mathematicallyand computationally easy to work with.
PB Elsevier
YR 2025
FD 2025-02
LK http://hdl.handle.net/10498/40378
UL http://hdl.handle.net/10498/40378
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 05-nov-2026