Hyperstability of the Jensen functional equation in ultrametric spaces

In this paper, we present hyperstability results of Jensen functional equations in ultrametric Banach spaces.     

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 hyperstability of {\sigma}-Drygas functional equation on semigroups

In this paper, we obtain hyperstability results for the \({\sigma}\)-Drygas functional equation and the inhomogeneous \({\sigma}\)-Drygas functional equation on semigroups. Namely, we show that a function satisfying the \({\sigma}\)-Drygas equation approximately must be exactly the solution of it.     

Stability of an $$\varvec{}{}$$th root functional equation in $$\varvec{C}^{*}$$C∗-algebras: a fixed point approach

In this paper, we introduce an \(m{\text{th}}\) root functional equation. Using the fixed point approach, we prove the Hyers–Ulam stability of the \(m{\text{th}}\) root functional equation in \(C^{*}\)-algebras.     

Hyperstability results for a generalized radical cubic functional equation related to additive mapping in non-Archimedean Banach spaces

The aim of this paper is to introduce and solve the following generalized radical cubic functional equation

$$\begin{aligned} f\left( \root 3 \of {\sum _{i=1}^{k}x_{i}^{3}}\right) =\sum _{i=1}^{k}f(x_{i}),\quad k\in \mathbb {N}_{2}. \end{aligned}$$

We also investigate some hyperstability results for this equation in non-Archimedean Banach spaces.