Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Fuzzy Hyers-Ulam stability of an additive functional equation | Kenary et al. Journal of Inequalities and Applications 2011 2011 140 http content 2011 1 140 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Fuzzy Hyers-Ulam stability of an additive functional equation Hassan Azadi Kenary 1 Hamid Rezaei1 Anoshiravan Ghaffaripour1 Saedeh Talebzadeh2 Choonkil Park3 and Jung Rye Lee4 Correspondence jrlee@. kr department of Mathematics Daejin University Kyeonggi 487711 Korea Full list of author information is available at the end of the article Abstract In this paper using the fixed point and direct methods we prove the Hyers-Ulam stability of the following additive functional equation x y z 2f 2 f x f y f z in fuzzy normed spaces. Mathematics Subject Classification 2010 39B22 39B52 39B82 46S10 47S10 46S40. Keywords Hyers-Ulam stability additive functional equation fuzzy normed space 1. Introduction A classical question in the theory of functional equations is the following When is it true that a function which approximately satisfies a functional equation must be close to an exact solution of the equation If the problem accepts a solution we say that the equation is stable. The first stability problem concerning group homomorphisms was raised by Ulam 1 in 1940. In the next year Hyers 2 gave a positive answer to the above question for additive groups under the assumption that the groups are Banach spaces. In 1978 Rassias 3 proved a generalization of the Hyers theorem for additive mappings. Theorem . . Rassias Let f X Y be a mapping from a normed vector space X into a Banach space Y subject to the inequality II f x y -f x - f y II s x p II ylld for all x y e X where and p are constants with 0 and 0 p 1. Then the limit L x lim r f 2nx 2n exists for all x e X and L X Y is the unique additive mapping which satisfies II f x L x 2s 2 - 2p II x p for all x e X. Also iffor each x e X the function f tx is continuous in t e R then L is .
