tailieunhanh - Báo cáo hóa học: " Fuzzy Stability of Generalized Mixed Type Cubic, Quadratic, and Additive Functional Equation"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Fuzzy Stability of Generalized Mixed Type Cubic, Quadratic, and Additive Functional Equation | Gordji et al. Journal of Inequalities and Applications 2011 2011 95 http content 2011 1 95 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Fuzzy Stability of Generalized Mixed Type Cubic Quadratic and Additive Functional Equation 1112 3 Madjid Eshaghi Gordji Mahdie Kamyar Hamid Khodaei Dong Yun Shin and Choonkil Park Correspondence baak@hanyang. department of Mathematics Research Institute For Natural Sciences Hanyang University Seoul 133-791 Korea Full list of author information is available at the end of the article Springer Abstract In this paper we prove the generalized Hyers-Ulam stability of generalized mixed type cubic quadratic and additive functional equation in fuzzy Banach spaces. 2010 Mathematics Subject Classification 39B82 39B52. Keywords fuzzy Hyers-Ulam stability mixed functional equation fuzzy normed space 1. Introduction The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative answer to the question of Ulam for Banach spaces. Hyers theorem was generalized by Aoki 3 for additive mappings and by Rassias 4 for linear mappings by considering an unbounded Cauchy difference. The paper of Rassias 4 has provided a lot of influence in the development of what we now call generalized Hyers-Ulam stability of functional equations. In 1994 a generalization of the Rassias theorem was obtained by Găvruta 5 by replacing the unbounded Cauchy difference by a general control function in the spirit of Rassias approach. The functional equation f x y f x - y 2f x 2f y is related to a symmetric bi-additive mapping 6 7 . It is natural that this equation is called a quadratic functional equation. In particular every solution of the quadratic equation is said to be a quadratic mapping. It is well known that a mapping f between real vector spaces is quadratic if and only if