Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 707406, 6 pages
doi:10.1155/2009/707406
Research Article

A Note on Implicit Functions in Locally Convex Spaces

Marianna Tavernise and Alessandro Trombetta

Dipartimento di Matematica, Università degli Studi della Calabria, 87036 Arcavacata di Rende (CS), Italy

Received 27 February 2009; Accepted 19 October 2009

Academic Editor: Fabio Zanolin

Copyright © 2009 Marianna Tavernise and Alessandro Trombetta. 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.

Abstract

An implicit function theorem in locally convex spaces is proved. As an application we study the stability, with respect to a parameter λ, of the solutions of the Hammerstein equation x=λKFx in a locally convex space.