To the problem of invertibility of quadratic mappings (Q2719490)

The classical Banach theorem solves the problem on boundedness of the right inverse operator for the linear operator acting from the Banach space into the Banach space. This paper addresses the problem on boundedness conditions for the right inverse operator for the surjective quadratic mapping. The author finds out exact conditions for the quadratic mappings from \(\mathbb{R}^n\to \mathbb{R}^n \) for \(n=1,2,3\).