We study the existence of an implicit function, defined by an equation G(x, σ) = 0, in a neighborhood of an abnormal point (x0, σ0). We prove that if some λ-truncation of the mapping F(x) = G(x, σ0) is regular in
a certain direction, then the sought implicit function exists.
Keywords:
implicit function, abnormal point, nonlinear equation, real solution, truncation, regularity in direction
