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 A Fixed Point Approach to the Fuzzy Stability of an Additive-Quadratic-Cubic Functional Equation | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 918785 24 pages doi 2009 918785 Research Article A Fixed Point Approach to the Fuzzy Stability of an Additive-Quadratic-Cubic Functional Equation Choonkil Park Department of Mathematics Research Institute for Natural Sciences Hanyang University Seoul 133-791 South Korea Correspondence should be addressed to Choonkil Park baak@ Received 23 August 2009 Revised 18 October 2009 Accepted 23 October 2009 Recommended by Fabio Zanolin Using the fixed point method we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic functional equation f x 2y f x - 2y 2f x y - 2f -x - y 2f x -y - 2f fy - x f 2y f -2y 4f -x - 2f x in fuzzy Banach spaces. Copyright 2009 Choonkil Park. 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 and Preliminaries Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2-4 . In particular Bag and Samanta 5 following Cheng and Mordeson 6 gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michalek type 7 . They established a decomposition theorem of a fuzzy norm into a family of crisp norms and investigated some properties of fuzzy normed spaces 8 . We use the definition of fuzzy normed spaces given in 5 9 10 to investigate a fuzzy version of the generalized Hyers-Ulam stability for the functional equation f x 2y f x - 2y - 2f x y - 2f -x - y 2f x - y - 2f y - x . f 2y f -2y 4f -x - 2f x in the fuzzy normed vector space setting. 2 Fixed Point Theory and Applications Definition see 5 9-11 . Let X be a real vector space. A function N X X R 0
