Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Fuzzy stability of a mixed type functional equation | Jin and Lee Journal of Inequalities and Applications 2011 2011 70 http content 2011 1 70 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Fuzzy stability of a mixed type functional equation Sun Sook Jin and Yang-Hi Lee Correspondence yanghi2@ Department of Mathematics Education Gongju National University of Education Gongju 314-711 Republic of Korea Springer Abstract In this paper we investigate a fuzzy version of stability for the functional equation f x y z f x y f y z f x z f x f y f z 0 in the sense of Mirmostafaee and Moslehian. 1991 Mathematics Subject Classification. Primary 46S40 Secondary 39B52. Keywords fuzzy normed space fuzzy almost quadratic-additive mapping mixed type functional equation Introduction A classical question in the theory of functional equations is when is it true that a mapping which approximately satisfies a functional equation must be somehow close to an exact solution of the equation . Such a problem called a stability problem of the functional equation was formulated by Ulam 1 in 1940. In the next year Hyers 2 gave a partial solution of Ulam s problem for the case of approximate additive mappings. Subsequently his result was generalized by Aoki 3 for additive mappings and by Rassias 4 for linear mappings for considering the stability problem with unbounded Cauchy differences. During the last decades the stability problems of functional equations have been extensively investigated by a number of mathematicians see 5-17 . In 1984 Katsaras 18 defined a fuzzy norm on a linear space to construct a fuzzy structure on the space. Since then some mathematicians have introduced several types of fuzzy norm in different points of view. In particular Bag and Samanta 19 following Cheng and Mordeson 20 gave an idea of a fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michalek type 21 . In 2008 Mirmosta-faee and Moslehian 22
