Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí sinh học đề tài :A fixed point approach to the Hyers-Ulam stability of a functional equation in various normed spaces | Kenary et al. Fixed Point Theory and Applications 2011 2011 67 http content 2011 1 67 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access A fixed point approach to the Hyers-Ulam stability of a functional equation in various normed spaces Hassan Azadi Kenary1 Sun Young Jang2 and Choonkil Park3 Correspondence baak@hanyang. department of Mathematics Research Institute for Natural Sciences Hanyang University Seoul 133-791 Korea Full list of author information is available at the end of the article Springer Abstract Using direct method Kenary Acta Universitatis Apulensis to appear proved the Hyers-Ulam stability of the following functional equation m n f x y m n f x y f mx ny ------- ------------------------ in non-Archimedean normed spaces and in random normed spaces where m n are different integers greater than 1. In this article using fixed point method we prove the Hyers-Ulam stability of the above functional equation in various normed spaces. 2010 Mathematics Subject Classification 39B52 47H10 47S40 46S40 30G06 26E30 46S10 37H10 47H40. Keywords Hyers-Ulam stability non-Archimedean normed space random normed space fuzzy normed space fixed point method 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 then we say that the equation is stable. The first stability problem concerning group homomorphisms was raised by Ulam 1 in 1940. In the following 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 Hyers theorem for additive mappings. Furthermore in 1994 a generalization of the Rassias theorem was obtained by Găvruta 4 by replacing the bound e x p y p by a general
