Equivalence of some geometric and related results of nonlinear functional analysis. (English) Zbl 0656.47050

Danes, J.

Commentat. Math. Univ. Carol. 26, 443-454 (1985).

The author’s drop theorem, generalized drop theorem, Krasnoselskij- Zabreǐko renorming theorem, Browder’s generalization of the Bishop- Phelps theorem, Ekeland’s variational principle and Caristi fixed point theorem are mutually equivalent.

MSC:

47H10	Fixed-point theorems
47J05	Equations involving nonlinear operators (general)
46B20	Geometry and structure of normed linear spaces

Keywords:

generalized drop theorem; Krasnoselskij-Zabreǐko renorming theorem; Bishop-Phelps theorem; Ekeland’s variational principle; Caristi fixed point theorem