Abstract

The objective of this paper is to present certain conditions guaranteeing invertibility of a nonlinear operator between normed linear spaces. The idea is to approximate the given operator by an invertible, possibly linear operator, and reduce the problem to the contraction mapping principle. Several theorems of this kind are given, which appear as generalizations of some early results by I.W. Sandberg, and estimates for an “approximate inverse” are established. Finally, introducing certain “invertibility indices,” further sufficient and necessary conditions for invertibility are given.

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