Abstract
Using a novel Wintner-type formulation of the classical Peano's existence theorem (Math. Ann. 37 (1890), 182-228), we enhance Wazewski's result on invertibility of maps defined on closed balls (Ann. Soc. Pol. Math. 20 (1947), 81-125) securing the size of the domain of invertibility that agrees with the bounds derived by John (Comm. Pure Appl. Math. 21 (1968), 77-110) and Sotomayor (Z. Angew. Math. Phys. 41 (1990), 306-310).
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