一类泛函方程的广义Hyers-Ulam稳定性  

Generalized Hyers-Ulam stability for a class of functional equation

作　　者：韩玥 成立花[1] HAN Yue;CHENG Lihua(School of Science,Xi'an Polytechnic University,Xi'an 710048,China)

机构地区：[1]西安工程大学理学院,西安710048

出　　处：《华中师范大学学报（自然科学版）》2024年第3期310-314,共5页Journal of Central China Normal University：Natural Sciences

基　　金：陕西省自然科学基础研究计划项目(2021JM-445).

摘　　要：该文结合差分算子的定义,给出二次、三次和四次泛函方程的统一形式,使得这个新的泛函方程涵括了Kayal、Tamilvanan和Alkhaldi等人的结论.然后利用经典的直接法和不动点法,研究该泛函方程在Banach空间上的Hyers-Ulam稳定性.最后,应用所得结论,改进与推广了几类已知二次、三次和四次泛函方程的稳定性结果.Combined with the definition of difference operator,the unified form of quadratic,cubic and quartic functional equations is given,which makes this new functional equation include the conclusions of Kayal,Tamilvanan and Alkhaldi,et al.Then,the Hyers-Ulam stability of the functional equation on Banach space is studied by using classical direct method and fixed point method.Finally,the stability results of known quadratic,cubic and quartic functional equations are improved and generalized by applying the conclusions.

关 键 词：HYERS-ULAM稳定性 直接法 不动点法 BANACH空间 

分 类 号：O177.7[理学—数学]