Some generic properties of α-nonexpansive mappings |
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Authors: | Tomás Domínguez Benavides |
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Affiliation: | Facultad de Matemáticas, c/ Tarfia s/n, Seville-12, Spain |
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Abstract: | Let X be a Banach space, C a bounded closed subset of X, A a convex closed subset of X, a complete metric space formed by all α-nonexpansive mappings fC → A and a complete metric space formed by α-nonexpansive differentiable mappings fC → X. The following assertions are proved in this paper: (1) Properness of I ? f is a generic property in (2)the subset of formed by all α-contractive mappings is of Baire first category in ; and (3) for every y?X, the functional equation x ? f(x) = y has generically a finite number of solutions for f in . Some applications to the fixed point theory and calculation of the topological degree are given. |
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