Remarks on the inverse and implicit function theorems for differentiable functions - Fenille, Marcio Colombo; Vellozo, Telmo Irineo Acosta (Boletín de la Sociedad Matemática Mexicana, 2021)
We propose a detailed description for the proofs of the key results that support the inverse function theorem for differentiable functions (presented by Radulescu and Radulescu in J Math Anal Appl 138(2):581–590, 1989), an extension for one of that results for continuous functions and a complete proof for that version of the inverse function theorem itself. Furthermore, by means of a technical strengthening of the hypothesis, we transmute an existence theorem for certain initial value problems, proposed by Biasi et al. (Topol Methods Nonlinear Anal 32(1), 177–186, 2008), to a uniqueness and existence theorem.