Local inversion theorem for singular points

On an Application of a Higher Order Inversion Theorem to Certain Integral Equations and Boundary Value Problems

“…In [4], [5] and [6], there is described a local and a global inversion theorem for mappings with a singular point in which several derivatives vanish. We shall apply them to integral equations and boundary value problems.…”

A global inversion theorem for functions with singular points

“…The following theorem proved in [1] (Theorem 6) describes conditions equivalent to those from the previous theorem: Theorem 2.2. Assuming the invertibility of f , condition (1) in Theorem 2.1 is valid if and only if there exists a constant C 1 > 0 such that…”

Covering properties at positive-order rates of multifunctions and some related topics

“…To reveal the property, one may use the higher-order variations in the sense of Frankowska [3], the higher-order coderivatives in the sense of Mordukhovich [11], and other higher-order approximation constructions. For single-valued mappings, one may use higher-order Fréchet derivatives [2].…”