Implicit function theorem without a priori assumptions about normality

  • A. V. Arutyunov


The equation F(x, σ) = 0,xK, 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.


implicit function theory 2-regularity condition Robinson condition convex cone 


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Copyright information

© MAIK “Nauka/Interperiodica” 2006

Authors and Affiliations

  • A. V. Arutyunov
    • 1
  1. 1.Peoples Friendship UniversityMoscowRussia

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