Geodesic
Weakly coercive mappings sharing a value
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 1, pp. 65-72.

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Some sufficient conditions are provided that guarantee that the difference of a compact mapping and a proper mapping defined between any two Banach spaces over $\mathbb {K}$ has at least one zero. When conditions are strengthened, this difference has at most a finite number of zeros throughout the entire space. The proof of the result is constructive and is based upon a continuation method.
DOI : 10.1007/s10587-011-0017-y
Classification : 47J07, 58C15, 58C30, 65H10, 65J15
Keywords: zero point; continuation method; $C^{1}$-homotopy; surjerctive implicit function theorem; proper mapping; compact mapping; coercive mapping; Fredholm mapping 
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Soriano, J. M. Weakly coercive mappings sharing a value. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 1, pp. 65-72. doi : 10.1007/s10587-011-0017-y. http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0017-y/

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