关于Jensen泛函方程Hyers-Ulam稳定性的一个结论  

A Conclusion about the Hyers-Ulam Stability of Jensen Functional Equation

作　　者：宋爱民[1] 

机构地区：[1]甘肃民族师范学院数学系,甘肃合作747000

出　　处：《甘肃高师学报》2016年第6期1-4,共4页Journal of Gansu Normal Colleges

基　　金：甘肃省高等学校科研项目(2015B-120)

摘　　要：对于Jensen泛函方程的Hyers-Ulam稳定性的证明,S.-M.Jung在1998年完成了对0≤p<1及p>1情形的证明,并给出反例说明当p=1时,Jensen泛函方程不具有Hyers-Ulam稳定性.利用Janusz Brzdek给出的一个不动点方法讨论Jensen泛函方程当p<0时的情形,并给出了结论,同时进一步讨论其在限定区域上的Hyers-Ulam稳定性.S.M.Jung had Proved the Hyers-Ulam stability of Jensen functional equation in 1998 for the case 0≤P〈1 and P〉1,and gave an counterexamples to prove that while P=I Jensen functional equation didn＇t have the character of Hyers-Ulam stability. In this article we u- sed a method of fixed point theorem that proved by Janusz Brzdek and proved the Jensen functional equation for the case P〈0, and gave a conclusion,while proved its Hyers-Ulam on a restrrict domain.

关 键 词：Jensen泛函方程 HYERS-ULAM稳定性 不动点方法 

分 类 号：O177.1[理学—数学]