Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Comment on “on the stability of quadratic double centralizers and quadratic multipliers: a fixed point approach” [Bodaghi et al., j. inequal. appl. 2011, article id 957541 (2011)] | Park et al. Journal of Inequalities and Applications 2011 2011 104 http content 2011 1 104 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Comment on on the stability of quadratic double centralizers and quadratic multipliers a fixed point approach Bodaghi et al. j. inequal. appl. 2011 article id 957541 2011 Choonkil Park 1 Jung Rye lee2 Dong Yun Shin3 and Madjid Eshaghi Gordji4 Correspondence madjid. eshaghi@ 4Department of Mathematics Semnan University P. O. Box 35195-363 Semnan Iran Full list of author information is available at the end of the article Springer Abstract Bodaghi et al. On the stability of quadratic double centralizers and quadratic multipliers a fixed point approach. J. Inequal. Appl. 2011 Article ID 957541 9pp. 2011 proved the Hyers-Ulam stability of quadratic double centralizers and quadratic multipliers on Banach algebras by fixed point method. One can easily show that all the quadratic double centralizers L R in the main results must be 0 0 . The results are trivial. In this article we correct the results. 2010 MSC 39B52 46H25 47H10 39B72. Keywords quadratic functional equation multiplier double centralizer stability superstability 1. Introduction In 1940 Ulam 1 raised the following question concerning stability of group homomorphisms Under what condition does there exist an additive mapping near an approximately additive mapping Hyers 2 answered the problem of Ulam for Banach spaces. He showed that for Banach spaces X and Y if e 0 and f X Y such that II f x y - f x - f y s for all x y e X then there exists a unique additive mapping T X Y such that II f x - T x s x e X . Consider f X Y to be a mapping such that f tx is continuous in t e R for all x e X. Assume that there exist constant e 0 and p e 0 1 such that II f x y -f x -f y s x p II y p x e X . Rassias 3 showed that there exists a unique R-linear mapping T X Y such that 2s . II f x - T x _ II x p
