Stability Problem for Jensen-type Functional Equations of Cubic Mappings

In this paper, we establish the general solution and the generalized Hyers-Ulam-Rassias stability problem for a cubic Jensen-type functional equation,4f（（3x＋y）/4）＋4f（（x＋3y）/4）=6f（（x＋y）/2）＋f（x）＋f（y）,9f（（2x＋y/3）＋9f（（x＋2y）/3）=16f（（x＋y）/2＋f（x）＋f（y）in the spirit of D. H. Hyers, S. M. Ulam, Th. M. Rassias and P. Gaevruta.

On the Stability of a Mixed Functional Equation Deriving from Additive, Quadratic and Cubic Mappings

In this paper, we investigate the general solution and the Hyers–Ulam stability of the following mixed functional equation f（2x ＋ y） ＋ f（2x- y） = 2f（2x） ＋ 2f（x ＋ y） ＋ 2f（x- y）- 4f（x）- f（y）- f（-y）deriving from additive, quadratic and cubic mappings on Banach spaces.

Stability Problem of Hyers-Ulam-Rassias for Generalized Forms of Cubic Functional Equation

Let n≥2 be an integer number. In this paper, we investigate the generalized Hyers Ulam- Rassias stability in Banach spaces and also Banach modules over a Banach algebra and a C＊-algebra and the stability using the alternative fixed point of an n-dimensional cubic functional equation in Banach spaces：f（2∑j=1^n-1 xj＋xn）＋f（2∑j=1^n-1 xj-xn）＋4∑j=1^n-1f（xj）=16f（∑j=1^n-1 xj）＋2∑j=1^n-1（f（xj＋xn）＋f（xj-xn）

The Hyers-Ulam Stability of a Functional Equation Deriving from Quadratic and Cubic Functions in Quasi-β-normed Spaces

In this paper, we investigate the Hyers-Ulam stability of the following function equation 2f（2x ＋ y） ＋ 2f（2x - y） = 4f（x ＋ y） ＋ 4f（x - y） ＋ 4f（2x） ＋ f（2y） - Sf（x） - 8f（y） in quasi-β-normed spaces.

Banach空间中一类混合型泛函方程的稳定性

提出了一类新的三-四次混合型泛函方程,并得到它在向量空间中的通解。结合差分算子的定义,采用直接法证明了Banach空间上该混合型泛函方程的广义Hyers-Ulam-Rassias稳定性。

On the Stability of a Cubic Functional Equation

In this paper, we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for the following cubic functional equation2f（x ＋ 2y） ＋ f（2x - y） = 5f（x ＋ y） ＋ 5f（x - y）＋ 15f（y）in the spirit of Hyers, Ulam, Rassias and Gavruta.

Refined Functional Equations Stemming from Cubic,Quadratic and Additive Mappings

Let n ≥ 2 be an integer. In this paper, we investigate the generalized Hyers-Ulam stability problem for the following functional equation f（n-1∑j=1 xj＋2xn）＋f（n-1∑j=1 xj-2xn）＋8 n-1∑j=1f（xj）=2f（n-1∑j=1 xj） ＋4 n-1∑j=1[f（xj＋xn）＋f（xj-xn）] which contains as solutions cubic, quadratic or additive mappings.

一类源自二次和三次映射的混合泛函方程的模糊稳定性

研究了泛函方程2f(2x+y)+2f(2x-y)=4f(x+y)+4f(x-y)+4f(2x)+f(2y)-8f(x)-8f(y)在模糊Banach空间中的Hyers-Ulam稳定性.