On Isac’s fixed point theorem for selfmaps of a Galerkin cone. (English. Extended French abstract) Zbl 0823.47057

Jachymski, Jacek

Ann. Sci. Math. Qué. 18, No. 2, 169-171 (1994).

Summary: Recently, using complementarity theory, G. Isac has proved a fixed point theorem for some class of self-maps of a Galerkin cone in a Hilbert space. In this note we extend this theorem to a case of self-maps of an arbitrary closed and convex (not necessarily bounded) subset of a reflexive Banach space.

MSC:

47H10	Fixed-point theorems
47J25	Iterative procedures involving nonlinear operators

Keywords:

self-maps of an arbitrary closed and convex not necessarily bounded subset of a reflexive Banach space; complementarity theory; fixed point theorem; self-maps of Galerkin cone in a Hilbert space