Kaskasem Prondanai, Klin-Eam Chakkrid
1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand.
2Research Center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok, Thailand.
J Inequal Appl. 2018;2018(1):236. doi: 10.1186/s13660-018-1824-6. Epub 2018 Sep 12.
In this paper, we prove Hyers-Ulam-Rassias stability of -algebra homomorphisms for the following generalized Cauchy-Jensen equation: for all and for any fixed positive integer , which was introduced by Gao et al. [ 3:63-77, 2009], on -algebras by using fixed poind alternative theorem. Moreover, we introduce and investigate Hyers-Ulam-Rassias stability of generalized -derivation for such functional equations on -algebras by the same method.
在本文中，我们利用不动点替代定理，证明了如下由高等人[3:63 - 77, 2009]引入的广义柯西 - 詹森方程在(C^) - 代数上的(C^) - 代数同态的海尔斯 - 乌拉姆 - 拉西亚斯稳定性：对于所有(x,y\in A)以及任意固定的正整数(n)。此外，我们用相同的方法引入并研究了(C^) - 代数上此类函数方程的广义(C^) - 导数的海尔斯 - 乌拉姆 - 拉西亚斯稳定性。
