Magdalena Piszczek

Hyperstability of the Drygas Functional Equation

We use the fixed point theorem for functional spaces to obtain the hyperstability result for the Drygas functional equation on a restricted domain. Namely, we show that a function satisfying the Drygas equation approximately must be exactly the solution of it.

Hyperstability of the Fréchet Equation and a Characterization of Inner Product Spaces

We prove some stability and hyperstability results for the well-known Frechet equation stemming from one of the characterizations of the inner product spaces. As the main tool, we use a fixed point theorem for the function spaces. We finish the paper with some new inequalities characterizing the inner product spaces.

On Approximately p-Wright Affine Functions in Ultrametric Spaces

We prove some results for mappings taking values in ultrametric spaces and satisfying approximately a generalization of the equation of p-Wright affine functions. They are motivated by the notion of stability for functional equations.

Selections of Set-valued Maps Satisfying Some Inclusions and the Hyers–Ulam Stability

We present a survey of several results on selections of some set-valued functions satisfying some inclusions and also on stability of those inclusions. Moreover, we show their consequences concerning stability of the corresponding functional equations.

On Stability of the Linear and Polynomial Functional Equations in Single Variable

We present a survey of selected recent results of several authors concerning stability of the following polynomial functional equation (in single variable)

Asymptotic stability of the Cauchy and Jensen functional equations

\varphi(x)=\sum_{i=1}^m a_i(x)\varphi(\xi_i(x))^{p(i)}+F(x),

Hyperstability of the Jensen functional equation

in the class of functions ϕ mapping a nonempty set S into a Banach algebra X over a field \(\mathbb{K}\in \{\mathbb{R},\mathbb{C}\}\), where m is a fixed positive integer, \(p(i)\in \mathbb{N}\) for \(i=1,\ldots,m\), and the functions \(\xi_i:S\to S\), \(F:S\to X\) and \(a_i:S\to X\) for \(i=1,\ldots,m\), are given. A particular case of the equation, with \(p(i)=1\) for \(i=1,\ldots,m\), is the very well-known linear equation