Estimating invertible domains of diffeomorphisms
In nonlinear analysis, the classical inverse function theorem provides sufficient conditions for a differentiable map to be invertible. However, the theorem only indicates the existence of an invertible neighborhood for the diffeomorphism. The present paper is concerned with estimates on the domain of invertibility for a diffeomorphism in Banach spaces. The results improve the estimates known in the literature (see, for example, [\textit{O. G. Mustafa} and \textit{Yu. V. Rogovchenko}, Proc. Am. Math. Soc. 135, No. 1, 69--75 (2007; Zbl 1116.34004)]). The main tool used in the paper is the continuation property of a diffeomorphism. An application of the obtained results to implicit function theorems is also given.
scientific article; zbMATH DE number 6135500
scientific article