Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : On nonlinear stability in various random normed spaces | Rassias et al. Journal of Inequalities and Applications 2011 2011 62 http content 2011 1 62 Journal of Inequalities and Applications a SpringerOpen Journal REVIEW Open Access On nonlinear stability in various random normed spaces John Michael Rassias1 Reza Saadati2 Ghadir Sadeghi3 and J Vahidi4 Correspondence RSAADATI@EML. CC department of Mathematics Science and Research Branch Islamic Azad University Tehran Iran Full list of author information is available at the end of the article Springer Abstract In this article we prove the nonlinear stability of the quartic functional equation 16f x 4y f 4x y 306 9f x y f x 2y j 136f x y 1394f x y 425f y 1530f x in the setting of random normed spaces Furthermore the interdisciplinary relation among the theory of random spaces the theory of non-Archimedean space the theory of fixed point theory the theory of intuitionistic spaces and the theory of functional equations are also presented in the article. Keywords generalized Hyers-Ulam stability quartic functional equation random normed space intuitionistic random normed space 1. Introduction The study of stability problems for functional equations is related to a question of Ulam 1 concerning the stability of group homomorphisms and affirmatively answered for Banach spaces by Hyers 2 . Subsequently this result of Hyers was generalized by Aoki 3 for additive mappings and by Rassias 4 for linear mappings by considering an unbounded Cauchy difference. The article of Rassias 4 has provided a lot of influence in the development of what we now call generalized Ulam-Hyers stability of functional equations. We refer the interested readers for more information on such problems to the article 5-17 . Recently Alsina 18 Chang et al. 19 Mirmostafaee et al. 20 21 Mihet and Radu 22 Mihet et al. 23 24 25 26 Baktash et al. 27 Eshaghi et al. 28 Saadati et al. 29 30 investigated the stability in the settings of fuzzy probabilistic and random normed .
