Global invertibility of mappings between Banach spaces and applications to nonlinear equations

TL;DR

This paper establishes sufficient conditions for mappings between Banach spaces to be diffeomorphisms, simplifying previous results and applying them to algebraic and integro-differential equations.

Contribution

It introduces new, simplified criteria for invertibility of Banach space mappings and extends previous work with broader applicability.

Findings

Provided new conditions for invertibility of mappings between Banach spaces.

Generalized previous results on diffeomorphisms in Banach spaces.

Applied the theoretical results to algebraic and integro-differential equations.

Abstract

We provide sufficient conditions for a mapping between two Banach spaces to be a diffeomorphism using the approach of an auxiliary functional and also by the aid of a duality mapping corresponding to a normalization function. We simplify and generalize our previous results. Applications to algebraic equations and to integro-differential systems are also given.