Stability of Jensen functional equation in intuitionistic fuzzy normed space

In this paper, we determine some stability results concerning the Jensen functional equation 2f((x+y)/2)=f(x)+f(y) in intuitionistic fuzzy normed spaces (IFNS). We define the intuitionistic fuzzy continuity of the Jensen mappings and prove that the existence of a solution for any approximately Jensen mapping implies the completeness of IFNS.     

On a problem of Schwaiger in random normed spaces

We consider a problem of Schwaiger in the setting of random normed spaces to obtain a characterization for the completeness of these spaces by means of the stability of the Cauchy additive functional equation.     

Stability of Pexiderized quadratic functional equation in intuitionistic fuzzy normed space

The object of the present paper is to determine the stability of the Hyers-Ulam-Rassias type theorem concerning the Pexiderized quadratic functional equation in intuitionistic fuzzy normed spaces (IFNS).     

Generalized Ulam-Hyers stability of random homomorphisms in random normed algebras associated with the Cauchy functional equation

Using the fixed point method, we prove the generalized Ulam-Hyers stability of random homomorphisms in random normed algebras associated with the Cauchy functional equation.     

On stability of the monomial functional equation in normed spaces over fields with valuation

A stability theorem is proved for the monomial functional equation where the functions map a normed space over a field of characteristic zero with an arbitrary valuation into a Banach space over a field of characteristic zero with a valuation. Some regularity properties of the monomial functions are also discussed.     

Stability of the quadratic functional equation in Lipschitz spaces

Let G be an Abelian group with a metric d and E a normed space. For any f:G→E we define the quadratic difference of the function f by the formula

Qf(x,y):=2f(x)+2f(y)−f(x+y)−f(x−y)     

Stability of multi-additive mappings in non-Archimedean normed spaces

A function f:Vn→W, where V is a commutative semigroup, W is a linear space and n?1 is an integer, is called multi-additive if it is additive in each variable. In this paper we prove the generalized Hyers-Ulam stability of multi-additive mappings in non-Archimedean normed spaces, using the so-called direct method.     

Stability of a mixed additive and cubic functional equation in quasi-Banach spaces

In this paper we establish the general solution and investigate the Hyers-Ulam-Rassias stability of the following functional equation

f(2x+y)+f(2x−y)=2f(x+y)+2f(x−y)+2[f(2x)−2f(x)]     

Stability of a mixed additive and quadratic functional equation in quasi-Banach spaces

We study the stability of functional equations in quasi-Banach spaces where the quasi-norm is not assumed to be a p-norm. To overcome the modulus of concavity greater than 1 and the discontinuity of quasi-norms we use the squeeze inequality presented in an explicit revision of Aoki–Rolewicz Theorem  [13, Theorem 1]. As illustrations, we prove an extension of the stability of a mixed additive and quadratic functional equation in p-Banach spaces to quasi-Banach spaces with better approximation. The technique may be used to prove extensions of other results on the stability of functional equations in p-Banach spaces to quasi-Banach spaces.     

Stability for quadratic functional equation in the spaces of generalized functions

In this paper, we consider the general solution of quadratic functional equation

f(ax+y)+f(ax−y)=f(x+y)+f(x−y)+2(a²−1)f(x)     

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.     

Stability of preserving lattice cubic functional equation in Menger probabilistic normed Riesz spaces

The aim of this paper is to investigate Hyers–Ulam–Rassias stability of preserving lattice functional equation in various spaces. First, we prove stability of generalized preserving lattice functional equation in Banach lattices. Next, we show stability of preserving lattice cubic functional equation in Menger probabilistic normed Riesz spaces.     

Stability of a cubic functional equation in fuzzy normed space

In this paper, the authors investigate the general solution of a new cubic functional equation \(\begin{equation*} 3f(x+3y)-f(3x+y)=12[f(x+y)+f(x-y)]+80f(y)-48f(x) \end{equation*}\) and discuss its generalized Hyers - Ulam - Rassias stability in Banach spaces and stability in fuzzy normed spaces.     

Stability of mixed additive-quadratic Jensen type functional equation in non-Archimedean \ell -fuzzy normed spaces

In this papers we prove the generalized Hyers–Ulam–Rassias stability of the following mixed additive-quadratic Jensen functional equation $$\begin{aligned} 2f\left( \frac{x+y}{2}\right) +f\left( \frac{x-y}{2}\right) +f\left( \frac{y-x}{2}\right) =f(x)+f(y) \end{aligned}$$ in non- Archimedean \(\ell \) -fuzzy normed spaces.     

Stability of the generalized quadratic and quartic type functional equation in non-Archimedean fuzzy normed spaces

In this paper, we prove some stability results concerning the generalized quadratic and quartic type functional equation in the context of non-Archimedean fuzzy normed spaces in the spirit of Hyers-Ulam-Rassias. As applications, we establish some results of approximately generalized quadratic and quartic type mapping in non-Archimedean normed spaces. Also, we show that the assumption of the non-Archimedean absolute value of $2$ is less than $1$ cannot be omitted in our corollaries. The results improve and extend some recent results.     

On stability of a cubic functional equation in intuitionistic fuzzy normed spaces

In this paper, we determine some stability results concerning the cubic functional equation

f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x)