A study on Davison’s functional equation for set-valued functions

IF 0.7 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2025-04-16 DOI:10.1007/s00010-025-01157-6

Elham Mohammadi, Abbas Najati, Iz-iddine EL-Fassi

引用次数: 0

Abstract

Let X be a unital algebra with unit e and Y a real Hausdorff topological vector space. In this article, we obtain the general set-valued solution of the Davison functional equation

$$\begin{aligned} F(xy+x)+F(y)=F(xy)+F(x+y) \end{aligned}$$

for functions F defined on X with values in the set of nonempty compact and convex subsets of Y. Additionally, we investigate various extensions of the Davison set-valued functional equation.

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集值函数Davison泛函方程的研究

设X是一个单位代数，其单位为e， Y是一个实的Hausdorff拓扑向量空间。本文得到了定义在X上的函数F的一般集值解$$\begin{aligned} F(xy+x)+F(y)=F(xy)+F(x+y) \end{aligned}$$，函数F的值在y的非空紧子集和凸子集的集合中。此外，我们研究了Davison集值泛函方程的各种扩展。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.