Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Nonlinear approximation of an ACQ-functional equation in nan-spaces | Azadi Kenary et al. Fixed Point Theory and Applications 2011 2011 60 http content 2011 1 60 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Nonlinear approximation of an ACQ-functional equation in nan-spaces Hassan Azadi Kenary1 Jung Rye Lee2 and Choonkil Park3 Correspondence jrlee@. kr department of Mathematics Daejin University Kyeonggi 487711 Korea Full list of author information is available at the end of the article Springer Abstract In this paper using the fixed point and direct methods we prove the generalized Hyers-Ulam stability of an additive-cubic-quartic functional equation in NAN-spaces. Mathematics Subject Classification 2010 39B52-47H10-26E30-46S10-47S10 Keywords generalized Hyers-Ulam stability non-Archimedean normed space fixed point method 1. Introduction and preliminaries 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. The result of Rassias has provided a lot of influence during the last three decades in the development of a generalization of the Hyers-Ulam stability concept. This new concept is known as generalized Hyers-Ulam stability or Hyers-Ulam-Rassias stability of functional equations see 4-8 . Furthermore in 1994 a generalization of the Rassias theorem was obtained by Găvruta 9 by replacing the bound e x p y p by a general control function ộ x y . The functional equation f x y f x - y 2f x 2f y is called a quadratic
