Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Fixed Point Methods for the Generalized Stability of Functional Equations in a Single Variable | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 749392 15 pages doi 2008 749392 Research Article Fixed Point Methods for the Generalized Stability of Functional Equations in a Single Variable Liviu Cadariu1 and Viorel Radu2 1 Departamentul de Matematicd Universitatea Politehnica din Timi oara Piaịa Victoriei no. 2 300006 Timi oara Romania 2Facultatea de Matematicữ i Informaticd Universitatea de Vest din Timi oara Bv. Vasile Parvan 4 300223 Timi oara Romania Correspondence should be addressed to Liviu Cadariu Received 4 October 2007 Accepted 14 December 2007 Recommended by AndrzejSzulkin 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. Copyright 2008 L. Cadariu and V. 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. 1. Introduction and preliminaries The study of functional equations stability originated from a question of Ulam 1940 concerning the stability of group homomorphisms is as follows. Let G be a group endowed with a metric d. Given 0 does there exist a k 0 such that for every function f G G satisfying the inequality d f x y f x f y Vx y G G Ơ-1 there exists an automorphism a of G with d f x a x k Vx G G In 1941 Hyers 1 gave an affirmative answer to the question of Ulam for Cauchy equation in Banach spaces. Let E1 and E2 be Banach spaces and let f E1 E2 be such a mapping that f x y - f x - f y ô L3 2 Fixed Point Theory and .
