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: Generalized ulam-hyers stability of C*-Ternary algebra n-Homomorphisms for a functional equation | Park and Bae Journal of Inequalities and Applications 2011 2011 30 http content 2011 1 30 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Generalized ulam-hyers stability of C -Ternary algebra n-Homomorphisms for a functional equation Won-Gil Park1 and Jae-Hyeong Bae2 Correspondence jhbae@ 2Humanitas College Kyung Hee University Yongin 446-701 Republic of Korea Full list of author information is available at the end of the article SpringerOpen0 Abstract In this article we investigate the Ulam-Hyers stability of C -ternary algebra n-homomorphisms for the functional equation f X1 1 X2 1 X1 n X2 n f Xi1 1 Xin n l ilf- -fin in C -ternary algebras. 2000 Mathematics Subject Classification Primary 39B82 46B03 47Jxx. Keywords n-homomorphisms C -ternary algebra 1. Introduction and preliminaries Ternary algebraic operations were considered in the nineteenth century by several mathematicians such as Cayley 1 who introduced the notion of cubic matrix which in turn was generalized by Kapranov et al. 2 . The simplest example of such nontrivial ternary operation is given by the following composition rule a b c ijk ữnilbljmcmkn i j k 1 2 N . 1 l m n N Ternary structures and their generalization the so-called n-array structures raise certain hopes in view of their applications in physics. Some significant physical applications are as follows see 3 1 The algebra of nonions generated by two matrices 0 1 0 0 0 1 1 0 0 010 Ĩ 2- 0 0 o o e 3 1 o2 0 0 was introduced by Sylvester as a ternary analog of Hamilton s quaternions 4 . 2 The quark model inspired a particular brand of ternary algebraic systems. The so-called Nambu mechnics is based on such structures 5 . There are also some applications although still hypothetical in the fractional quantum Hall effect the non-standard statistics supersymmetric theory and Yang-Baxter equation 4 6 . 2011 Park and Bae licensee Springer. This is an Open Access .
