Title: A fixed point method for perturbation of bimultipliers and Jordan bimultipliers in C∗-ternary algebras
Abstract:Let A be a C∗-ternary algebra. A C-bilinear T:A×A→A is called a C∗-ternary algebra bi-multiplier, if it satisfies T([abc],d)=[T(a,b)cd], T(a,[bcd])=[abT(c,d)] for all a,b,c,d∊A. Also, the mapping T:A×...Let A be a C∗-ternary algebra. A C-bilinear T:A×A→A is called a C∗-ternary algebra bi-multiplier, if it satisfies T([abc],d)=[T(a,b)cd], T(a,[bcd])=[abT(c,d)] for all a,b,c,d∊A. Also, the mapping T:A×A→A is a called C∗-ternary algebra Jordan bimultiplier, if it satisfies T([aaa],a)=[T(a,a)aa], T(a,[aaa])=[aaT(a,a)] for all a∊A. Using the fixed point method, we investigate the generalized Hyers–Ulam–Rassias stability of bimultipliers and Jordan bimultipliers in C∗-ternary algebras. The concept of Hyers–Ulam–Rassias stability originated from the Th.M. Rassias’ stability theorem that appeared in his paper: [Th. M. Rassias, Proc. Am. Math. Soc. 72, 297 (1978)].Read More