Open Access

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

Fixed Point Theory and Applications20062006:92429

DOI: 10.1155/FPTA/2006/92429

Received: 31 January 2005

Accepted: 10 October 2005

Published: 20 April 2006


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.


Authors’ Affiliations

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


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© Vadim Azhmyakov. 2006

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