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 Solution and Stability of a Mixed Type Additive, Quadratic, and Cubic Functional Equation | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 826130 17 pages doi 2009 826130 Research Article Solution and Stability of a Mixed Type Additive Quadratic and Cubic Functional Equation M. Eshaghi Gordji 1 S. Kaboli Gharetapeh 2 J. M. Rassias 3 and S. Zolfaghari1 1 Department of Mathematics Semnan University . Box 35195-363 Semnan Iran 2 Department of Mathematics Payame Noor University of Mashhad Mashhad Iran 3 Section of Mathematics and Informatics Pedagogical Department National and Capodistrian University of Athens 4 Agamemnonos St. Aghia Paraskevi Athens 15342 Greece Correspondence should be addressed to M. Eshaghi Gordji Received 24 January 2009 Revised 13 April 2009 Accepted 26 June 2009 Recommended by Patricia J. Y. Wong We obtain the general solution and the generalized Hyers-Ulam-Rassias stability of the mixed type additive quadratic and cubic functional equation f x 2y - f x - 2y 2 f x y - f x - y 2f 3y - 6f 2y 6f y . Copyright 2009 M. Eshaghi Gordji et al. 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 stability problem of functional equations originated from a question of Ulam 1 in 1940 concerning the stability of group homomorphisms. Let G1z be a group and let G2 be a metric group with the metric d v . Given e 0 does there exist a Ỗ 0 such that if a mapping h G1 G2 satisfies the inequality d h x y h x hf-yf Ỗ for all x y e G1 then there exists a homomorphism H G1 G2 with d h x H x e for all x e G1 In other words under what condition does there exist a homomorphism near an approximate homomorphism In 1941 Hyers 2 gave a first affirmative answer to the question of Ulam for Banach spaces. Let f E E be a mapping between Banach spaces such that Ilf x y - f x - f y Ô for all x y e E and for some Ô 0.