Implicit function theorem without a priori assumptions about normality |
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Authors: | A. V. Arutyunov |
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Affiliation: | (1) Peoples Friendship University, ul. Miklukho-Maklaya 6, Moscow, 117198, Russia |
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Abstract: | The equation F(x, σ) = 0,x ∈ K, in which σ is a parameter and x is an unknown taking values in a given convex cone in a Banach space X, is considered. This equation is examined in a neighborhood of a given solution (x *, σ*) for which the Robinson regularity condition may be violated. Under the assumption that the 2-regularity condition (defined in the paper), which is much weaker than the Robinson regularity condition, is satisfied, an implicit function theorem is obtained for this equation. This result is a generalization of the known implicit function theorems even for the case when the cone K coincides with the entire space X. |
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Keywords: | implicit function theory 2-regularity condition Robinson condition convex cone |
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