Hindawi Publishing Corporation Advances in Difference Equations Volume 2008, Article ID 143053, 5 pages doi:10.1155/2008/143053 Research Article Stability of General Newton Functional Equations for Logarithmic Spirals Soon-Mo Jung 1 and John Michael Rassias 2 1 Mathematics Section, College of Science and Technology, Hong-Ik University, 339-701 Chochiwon, South Korea 2 Mathematics Section, Pedagogical Department EE, National and Capodistrian University of Athens, 4 Agamemnonos Street, Aghia Paraskevi, Athens, 15342 Attikis, Greece Correspondence should be addressed to Soon-Mo Jung, smjung@hongik.ac.kr Received 16 October 2007; Revised 8 January 2008; Accepted 25 January 2008 Recommended by Ulrich Krause We investigate the generalized Hyers-Ulam stability of Newton functional equations for logarith- mic spirals. Copyright q 2008 S.-M. Jung and J. M. Rassias. 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 The starting point of studying the stability of functional equations seems to be the famous talk of Ulam 1 in 1940, in which he discussed a number of important unsolved problems. Among those was the question concerning the stability of group homomorphisms. Let G 1 be a group and let G 2 be a metric group with a metric d·, ·. Given ε> 0, does there exist a δ> 0 such that if a mapping h : G 1 →G 2 satisfies the inequality dhxy,hxhy <δ for all x, y ∈ G 1 , then there exists a homomorphism H : G 1 →G 2 with dhx,Hx <ε for all x ∈ G 1 ? The case of approximately additive mappings was solved by Hyers 2 under the as- sumption that G 1 and G 2 are Banach spaces. Later, the result of Hyers was significantly gen- eralized for additive mappings by Aoki 3 and for linear mappings by Rassias 4. It should be remarked that we can find in the books 5–7 a lot of references concerning the stability of functional equations. Recently, Jung and Sahoo 8 proved the generalized Hyers-Ulam stability of the func- tional equation f  √ r 2  1 f r  arctan 1/r  which is closely related to the square root spiral, for the case that f 1 0 and f r  is monotone increasing for r> 0 see 9, 10.