框架的加性稳定性

Approximation of a Cauchy-Jensen additive mapping in various normed spaces

In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam-Rassias stability of a Cauchy-Jensen additive functional equation in various normed spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

Ulam stability of an additive-quadratic functional equation in F-space and quasi-Banach spaces

By adopting the direct method and fixed point method, we prove that the Hyers-Ulam stability of the following additive-quadratic functional equation \begin{equation} f(x+y, z+w)+f(x-y, z-w)-2 f(x, z)-2 f(x, w)=0 \end{equation} in $β$-homogeneous $F$-spaces and quasi-Banach spaces. There are some differences that we consider the target space with the $β$-homogeneous norm and quasi-norm. Overcoming the $β$-homogeneous norm and quasi-norm bottlenecks, we get some new results.

Stability of additive functional equation on discrete quantum semigroups

We show that noncommutative analog of additive functional equation has Hyers-Ulam stability on amenable discrete quantum (semi)groups. This generalizes an old classical result.

Stability Threshold for Multiadditive and Symmetric Mappings

We extend the Z. Gajda's result concerning the stability threshold for additive mappings to the n-additive and symmetric functions.

混合型加性-三次Jensen泛函方程在非阿基米德$(n, β)$赋范空间中的稳定性

Stability of Mixed Type Additive-Cubic Jensen Functional Equation in Non-Archimedean $(n, β)$ Normed Spaces

本文研究了混合型加性-三次Jensen泛函方程在非阿基米德$(n, β)$赋范空间中的Hyers-Ulam稳定性。

Stability of set-valued generalized additive Cauchy functional equation

The main purpose of this paper is to determine the solution of generalized convex set-valued mappings satisfying certain functional equation. Some conclusions of stability of set-valued functional equations are obtained.

Bi-additive s-functional inequalities and biderivations in modular spaces

In this article, by using the fixed point method, we prove the generalized Hyers--Ulam stability of biderivations from an algebra to a modular space, associated to bi-additive s-functional inequalities.

带参数的函数方程的Hyers-Ulam-Rassias稳定性

Hyers-Ulam-Rassias stability of functional equations with parameters

本文在β-齐次F-空间中研究广义Jensen加性和二次函数方程的Hyers-Ulam稳定性，证明近似映射存在唯一精确近似解。

A Fixed Point Approach to Stability of a Quadratic Equation

Using the fixed point alternative theorem we establish the orthogonal stability of quadratic functional equation of Pexider type $f(x+y)+g(x-y)=h(x)+k(y)$, where $f, g, h, k$ are mappings from a symmetric orthogonality space to a Banach space, by orthogonal additive mappings under a necessary and sufficient condition on $f$.