Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 92429, 17 pages
A fixed point theorem for a class of
differentiable stable operators in banach
Fakultät IV--Elektrotechnik und Informatik, Institut für Energie und Automatisierungstechnik, Technische
Universität Berlin, Sekretariat EN 11, Einsteinufer 17, Berlin 10587, Germany
Received 31 January 2005; Accepted 10 October 2005
Copyright © 2006 Vadim Azhmyakov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study Frèchet differentiable stable operators in real Banach
spaces. We present the theory of linear and nonlinear stable
operators in a systematic way and prove solvability theorems for
operator equations with differentiable expanding operators. In
addition, some relations to the theory of monotone operators in
Hilbert spaces are discussed. Using the obtained solvability
results, we formulate the corresponding fixed point theorem for a
class of nonlinear expanding operators.