Ulam Stabilities and Instabilities of Euler–Lagrange-Rassias Quadratic Functional Equation in Non-Archimedean IFN spaces

In this paper, we use direct and fixed-point techniques to examine the generalised Ulam–Hyers stability results of the general Euler–Lagrange quadratic mapping in non-Archimedean IFN spaces (briefly, non-Archimedean Intuitionistic Fuzzy Normed spaces) over a field.

Hyers-Ulam Stability of Quadratic Functional Equation Based on Fixed Point Technique in Banach Spaces and Non-Archimedean Banach Spaces

In this paper, the authors investigate the Hyers–Ulam stability results of the quadratic functional equation in Banach spaces and non-Archimedean Banach spaces by utilizing two different techniques in terms of direct and fixed point techniques.

Characterization and stability analysis of advanced multi-quadratic functional equations

In this paper, we introduce a new quadratic functional equation and, motivated by this equation, we investigate n-variables mappings which are quadratic in each variable. We show that such mappings can be unified as an equation, namely, multi-quadratic functional equation. We also apply a fixed point technique to study the stability for the multi-quadratic functional equations. Furthermore, we present an example and a few corollaries corresponding to the stability and hyperstability outcomes.

On alienation of two functional equations of quadratic type

We deal with an alienation problem for an Euler–Lagrange type functional equation $$\begin{aligned} f(\alpha x + \beta y) + f(\alpha x - \beta y) = 2\alpha ^2f(x) + 2\beta ^2f(y) \end{aligned}$$ f ( α x + β y ) + f ( α x - β y ) = 2 α 2 f ( x ) + 2 β 2 f ( y ) assumed for fixed nonzero real numbers $$\alpha ,\beta ,\, 1 \ne \alpha ^2 \ne \beta ^2$$ α , β , 1 ≠ α 2 ≠ β 2 , and the classic quadratic functional equation $$\begin{aligned} g(x+y) + g(x-y) = 2g(x) + 2g(y). \end{aligned}$$ g ( x + y ) + g ( x - y ) = 2 g ( x ) + 2 g ( y ) . We were inspired by papers of Kim et al. (Abstract and applied analysis, vol. 2013, Hindawi Publishing Corporation, 2013) and Gordji and Khodaei (Abstract and applied analysis, vol. 2009, Hindawi Publishing Corporation, 2009), where the special case $$g = \gamma f$$ g = γ f was examined.

On the Hyers–Ulam stability and hyperstability of a generalized quadratic functional equation in n-Banach spaces

In this paper, we establish some Hyers–Ulam stability and hyperstability results of the following functional equation [Formula: see text] in the class of functions from an abelian group [Formula: see text] into a [Formula: see text]-Banach space.

A New Approach to Hyers-Ulam Stability of r -Variable Quadratic Functional Equations

In this paper, we investigate the general solution of a new quadratic functional equation of the form ∑ 1 ≤ i < j < k ≤ r ϕ l i + l j + l k = r − 2 ∑ i = 1 , i ≠ j r ϕ l i + l j + − r 2 + 3 r − 2 / 2 ∑ i = 1 r ϕ l i . We prove that a function admits, in appropriate conditions, a unique quadratic mapping satisfying the corresponding functional equation. Finally, we discuss the Ulam stability of that functional equation by using the directed method and fixed-point method, respectively.

On the stability of a quadratic functional equation over non-Archimedean spaces

Let G be an abelian group and suppose that X is a non-Archimedean Banach space. We study Hyers-Ulam-Rassias stability for the functional equation of quadratic type f(x+y+z)+ f(x)+f(y)+f(z)=f(x+y)+f(y+z)+ f(z+x) where f : G ? X is a map.

An additive-quadratic functional equation in intuitionistic fuzzy normed spaces

In this work, we investigate the stability of additive-quadratic (AQ) functional equation in intuitionistic fuzzy normed spaces