Banach空间中一类泛函方程的Ulam稳定性

Ulam stability of a class of functional equations in Banach spaces

结合差分算子的定义,给出二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Lee、Kayal和玉强等的结论。然后利用经典的不动点法,研究该泛函方程在Banach空间上的Ulam稳定性。最后,应用定理1.1和定理1.2所得结论,改进并推广几类已知二次和四次泛函方程的稳定性结果。

Combined with the definition of difference operator,a unified form of quadratic and quartic functional equation was given,which included the conclusions of Lee,Kayal,Yu Qiang,etc.Then the Ulam stability of the functional equation on Banach space was studied by using the classical fixed-point method.Finally,the stability results of some quadratic and quartic functional equations were improved and generalized by applying the conclusions of Theorems 1.1 and 1.2.