Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 749392, 15 pages
doi:10.1155/2008/749392
Research Article
Fixed Point Methods for the Generalized Stability of Functional Equations in a Single Variable
1Departamentul de Matematică, Universitatea Politehnica din Timişoara, Piaţa Victoriei no. 2, 300006 Timişoara, Romania
2Facultatea de Matematică Şi Informatică, Universitatea de Vest din Timişoara, Bv. Vasile Pârvan 4, 300223 Timişoara, Romania
Received 4 October 2007; Accepted 14 December 2007
Academic Editor: Andrzej Szulkin
Copyright © 2008 Liviu Cădariu and Viorel Radu. 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
We discuss on the generalized Ulam-Hyers stability for functional equations in a single variable, including the nonlinear functional equations, the linear functional equations, and a generalization of functional equation for the square root spiral. The stability results have been obtained by a fixed point method. This method introduces a metrical context and shows that the stability is related to some fixed point of a suitable operator.