Open Access

A fixed point theorem for a class of differentiable stable operators in banach spaces

Fixed Point Theory and Applications20062006:92429

https://doi.org/10.1155/FPTA/2006/92429

Received: 31 January 2005

Accepted: 10 October 2005

Published: 20 April 2006

Abstract

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.

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Authors’ Affiliations

(1)
Fakultät IV--Elektrotechnik und Informatik, Institut für Energie und Automatisierungstechnik, Technische Universität Berlin

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Copyright

© Vadim Azhmyakov. 2006

This article is published under license to BioMed Central Ltd. 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.