On the Cauchy-Rassias stability of a generalized additive functional equation

Let X and Y be Banach spaces and f:X→Y an odd mapping. We solve the following generalized additive functional equation

     

On a generalized nonlinear functional equation

The paper deals with the functional equation

f(x)=F(f(u(x)),f(v(x)))     

On the Hyers-Ulam-Rassias stability of an additive functional equation in quasi-Banach spaces

In this paper we investigate the Hyers-Ulam-Rassias stability of the following functional equation:

     

On the stability of the additive Cauchy functional equation in random normed spaces

In this paper, we prove a stability result for the additive Cauchy functional equation in random normed spaces, related to the main theorem from the paper [D. Mihe?, V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl. 343 (2008) 567–572].     

On the stability of the additive Cauchy functional equation in random normed spaces

Some stability results for the functional equations of Cauchy and Jensen in probabilistic setting are proved by using the fixed point method.     

The generalized Hyers-Ulam-Rassias stability of a cubic functional equation

In this paper, we obtain the general solution and the generalized Hyers-Ulam stability for a cubic functional equation f(2x+y)+f(2x−y)=2f(x+y)+2f(x−y)+12f(x).     

Solution and stability of generalized mixed type additive and quadratic functional equation in non-Archimedean spaces

In this paper, we achieve the general solution and the generalized Hyres–Ulam–Rassias stability of the following additive–quadratic functional equation for fixed integers k with k≠0,±1 in the quasi-Banach spaces.     

17.

On the generalized d’Alembert functional equation     

Allal Bakali  Belaid Bouikhalene 《Aequationes Mathematicae》2006,71(3):209-227

     

18.

On a Cauchy-Jensen functional equation and its stability     

Won-Gil Park 《Journal of Mathematical Analysis and Applications》2006,323(1):634-643

In this paper, we obtain the general solution and stability of the Cauchy-Jensen functional equation

     

19.

On a bi-quadratic functional equation and its stability     

《Nonlinear Analysis: Theory, Methods & Applications》2005,62(4):643-654

     

20.

On the stability of a generalization of Jensen functional equation     

M. Almahalebi 《Acta Mathematica Hungarica》2018,154(1):187-198

Using the fixed point method, we investigate the stability of a generalization of Jensen functional equation

$$ \sum_{k=0}^{n-1} f(x+ b_{k}y)=nf(x),$$

where \({n \in \mathbb{N}_{2}}\), \({b_{k}=\exp(\frac{2i\pi k}{n})}\) for \({0\leq k \leq n-1}\), in Banach spaces. Also, we prove the hyperstability results of this equation by the fixed point method.

     

On a Cauchy-Jensen functional equation and its stability

In this paper, we obtain the general solution and stability of the Cauchy-Jensen functional equation

     

On the stability of a generalization of Jensen functional equation

Using the fixed point method, we investigate the stability of a generalization of Jensen functional equation

$$ \sum_{k=0}^{n-1} f(x+ b_{k}y)=nf(x),$$

where \({n \in \mathbb{N}_{2}}\), \({b_{k}=\exp(\frac{2i\pi k}{n})}\) for \({0\leq k \leq n-1}\), in Banach spaces. Also, we prove the hyperstability results of this equation by the fixed point method.

     

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 equation
2f（x ＋ 2y） ＋ f（2x - y） = 5f（x ＋ y） ＋ 5f（x - y）＋ 15f（y）
in the spirit of Hyers, Ulam, Rassias and Gavruta.     

On the stability of a quartic functional equation

In this paper, we prove the generalized Hyers-Ulam stability for the following quartic functional equation

f(2x+y)+f(2x−y)=4f(x+y)+4f(x−y)+24f(x)−6f(y).     

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.     

On the stability of some functional equations for generalized hyperbolic functions and for the generalized cosine equation

Two stability results concerning a system of functional equations for generalized hyperbolic and trigonometric functions on the one hand, and a generalized cosine equation on the other hand are presented.     

Solution and stability of generalized mixed type cubic, quadratic and additive functional equation in quasi-Banach spaces

In this paper, we achieve the general solution and the generalized Hyers–Ulam–Rassias stability of the following functional equation

f(x+ky)+f(x−ky)=k²f(x+y)+k²f(x−y)+2(1−k²)f(x)