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 Intuitionistic Fuzzy Stability of a Quadratic Functional Equation | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 107182 7 pages doi 2010 107182 Research Article Intuitionistic Fuzzy Stability of a Quadratic Functional Equation Liguang Wang School of Mathematical Sciences Qufu Normal University Qufu 273165 China Correspondence should be addressed to Liguang Wang wangliguang0510@ Received 6 October 2010 Accepted 23 December 2010 Academic Editor B. Rhoades Copyright 2010 Liguang Wang. 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. We consider the intuitionistic fuzzy stability of the quadratic functional equation f kx y f kx-y 2k2f x 2f y by using the fixed point alternative where k is a positive integer. 1. Introduction The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for Banach spaces. Hyers s theorem was generalized by Aoki 3 for additive mappings. In 1978 Rassias 4 generalized Hyers theorem by obtaining a unique linear mapping near an approximate additive mapping. Assume that E1 and E2 are real-normed spaces with E2 complete f E1 E2 is a mapping such that for each fixed x e E1 the mapping t f tx is continuous on R and there exist e 0 and p e 0 1 such that Ilf x y - f x - f y ll e x p y p M for all x y e E1. Then there is a unique linear mapping T E1 E2 such that 2e Ilf x - T x pAAp x p I2 - 2pI for all x e E1. 2 Fixed Point Theory and Applications The paper of Rassias has provided a lot of influence in the development of what we called the generalized Hyers-Ulam-Rassias stability of functional equations. In 1990 Rassias 5 asked whether such a theorem can also be proved for p 1. In 1991 Gajda 6 gave an affirmative solution to this question when p 1 but it
