%0 Journal Article
%A Ivanov, Milen
%A Jaramillo Aguado, Jesús Ángel
%A Lajara, Sebastián
%A Zlateva, Nadia
%T Continuous selections and invertibility of nonsmooth maps between Banach spaces
%D 2025
%@ 0022-3239
%@ 1573-2878
%U https://hdl.handle.net/20.500.14352/120656
%X In the setting of Banach spaces, we address the problems of local surjectivity, existence of a continuous selection and invertibility for nonsmooth maps which admit a suitable pseudo-Jacobian. We obtain a general sufficient condition for the existence of a continuous selection. As a consequence, we recover from our result the classical Bartle-Graves selection theorem for linear maps. We also obtain a sufficient condition for local invertibility, which in particular applies to certain Gâteaux differentiable maps.
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