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 On the Stability of a Generalized Quadratic and Quartic Type Functional Equation in Quasi-Banach Spaces | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 153084 26 pages doi 2009 153084 Research Article On the Stability of a Generalized Quadratic and Quartic Type Functional Equation in Quasi-Banach Spaces M. Eshaghi Gordji 1 S. Abbaszadeh 1 and Choonkil Park2 1 Department of Mathematics Semnan University . Box 35195-363 Semnan Iran 2 Department of Mathematics Research Institute for Natural Sciences Hanyang University Seoul 133-791 South Korea Correspondence should be addressed to Choonkil Park baak@ Received 31 May 2009 Accepted 9 September 2009 Recommended by Nikolaos Papageorgiou We establish the general solution of the functional equation f nx y f nx - y n2f x y n2f x - y 2 f nx - n2f x - 2 n2 - 1 f y for fixed integers n with n 0 1 and investigate the generalized Hyers-Ulam stability of this equation in quasi-Banach spaces. 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 G1 be a group and let G2 be a metric group with the metric d y . 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 xỴ e for all x e G1 In other words under what condition does there exist a homomorphism near an approximate homomorphism The concept of stability for functional equation arises when we replace the functional equation by an inequality which acts as a perturbation of the equation. In 1941 Hyers 2 gave a first affirmative answer to the question of Ulam for Banach spaces. Let f E E1 be a mapping between Banach spaces such that llf x y -
