An Observation Concerning the Application of the Contraction-Mapping Fixed-Point Theorem, and a Result Concerning the Norm-Boundedness of Solutions of Nonlinear Functional Equations

Let B denote a Banach space over the real or complex field F. Let (B) denote the set of (not necessarily linear) operators that map B into itself, with I the identity operator, and let $Vert T Vert$ denote the Lipshitz norm...