On the Ważewski equation. (English) Zbl 1002.58007

Olech, Czesław

Zesz. Nauk. Uniw. Jagiell. 1223, Univ. Iagell. Acta Math. 36, 55-64 (1998).

From the introduction: In 1947 Tadeusz Ważewski published a paper [Ann. Soc. Polon. Math. 20, 81-120 (1948; Zbl 0032.05601)] whose aim was to give an estimate for the domain of existence of the implicit functions, and of the inverse maps as a special case. The paper appeared in the same volume of Annales de la Société Polonaise de Mathématique which contains his celebrated retract method. In this note we discuss only this special case of the inverse map.

MSC:

58C15	Implicit function theorems; global Newton methods on manifolds
34A05	Explicit solutions, first integrals of ordinary differential equations
34D05	Asymptotic properties of solutions to ordinary differential equations
26B10	Implicit function theorems, Jacobians, transformations with several variables

Keywords:

implicit functions; inverse maps

Citations:

Zbl 0032.05601