Geodesic
Maps which are continuously differentiable in the sense of Michal and Bastiani but not of Fréchet
Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 63 (2017) no. 4, pp. 543-556 
H.-O. Walther. Maps which are continuously differentiable in the sense of Michal and Bastiani but not of Fréchet. Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 63 (2017) no. 4, pp. 543-556. http://geodesic.mathdoc.fr/item/CMFD_2017_63_4_a0/
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     author = {H.-O. Walther},
     title = {Maps which are continuously differentiable in the sense of {Michal} and {Bastiani} but not of {Fr\'echet}},
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     year = {2017},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2017_63_4_a0/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We construct examples of nonlinear maps on function spaces which are continuously differentiable in the sense of Michal and Bastiani but not in the sense of Frćhet. The search for such examples is motivated by studies of delay differential equations with the delay variable and not necessarily bounded.

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