%0 Journal Article 
%A Stefanini, Luciano
%A Arana Jiménez, Manuel
%A Sorini, Laerte
%T Fréchet and Gateaux gH-differentiability for interval valued functions of multiple variables
%D 2025
%U http://hdl.handle.net/10498/40378
%X 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.
%K Interval Valued Functions
%K gH-linearity
%K Fréchet gH-differentiability
%K Gateaux interval derivative
%K Interval gradient
%K Interval Jacobian and Hessian matrices
%~ Universidad de Cádiz