On a Domain of Invertibility of a Differentiable Mapping

Abstract

This paper deals with a domain and its range of invertibility of a differentiable mapping at a point with an invertible derivative. Assuming the C ²-class of a mapping T defined in a neighbourhood of a point x ₀ in Banach space with an invertible derivative, we look for estimations of radii of balls with centers in x ₀ and T (x ₀) which are contained in a domain of invertibility of T and its range, respectively.