Geodesic
Continuous mappings of open sets in a~Banach space
Matematičeskie zametki, Tome 13 (1973) no. 6, pp. 839-848.

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If $\Gamma$ is a bounded open set of a Banach space ($B$), $\varphi$ is a completely continuous mapping of $\Gamma$ into the same space ($B$), and $E-\varphi\equiv\Phi$, where E is the identity transformation, is a uniformly fading mapping of $\Gamma$ into the Banach space, then the order of $\Phi$ on $\Gamma$ equals $\pm1$ at every point $y$ of $\Phi\Gamma$. 
@article{MZM_1973_13_6_a5,
     author = {R. V. Belova},
     title = {Continuous mappings of open sets in {a~Banach} space},
     journal = {Matemati\v{c}eskie zametki},
     pages = {839--848},
     publisher = {mathdoc},
     volume = {13},
     number = {6},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_6_a5/}
}
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R. V. Belova. Continuous mappings of open sets in a~Banach space. Matematičeskie zametki, Tome 13 (1973) no. 6, pp. 839-848. http://geodesic.mathdoc.fr/item/MZM_1973_13_6_a5/