Article
MSC:
47J07,
58C15,
58C30,
65H10,
65J15 | MR 2782759 | Zbl 1224.58008 | DOI: 10.1007/s10587-011-0017-y
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Keywords:
zero point; continuation method; $C^{1}$-homotopy; surjerctive implicit function theorem; proper mapping; compact mapping; coercive mapping; Fredholm mapping
zero point; continuation method; $C^{1}$-homotopy; surjerctive implicit function theorem; proper mapping; compact mapping; coercive mapping; Fredholm mapping
Summary:
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.
References:
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