Generalized Vincze’s functional equations on any group in connection with the maximum functional equation

IF 0.9 3区 数学 Q2 MATHEMATICS Aequationes Mathematicae Pub Date : 2024-02-03 DOI:10.1007/s00010-023-01031-3
Muhammad Sarfraz, Zhou Jiang, Qi Liu, Yongjin Li
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Abstract

In this research paper, we investigate a generalization of Vincze’s type functional equations involving several (up to four) unknown functions in connection with the maximum functional equation as

$$\begin{aligned} \max \{\psi (xy), \psi (xy^{-1})\}&= \psi (x)\eta (y)+\psi (y), \\ \max \{\psi (xy), \psi (xy^{-1})\}&= \psi (x)\eta (y)+\chi (y), \\ \max \{\psi (xy), \psi (xy^{-1})\}&= \phi (x)\eta (y), \\ \max \{\psi (xy), \psi (xy^{-1})\}&= \phi (x)\eta (y)+\chi (y), \end{aligned}$$

where G is an arbitrary group, \(x, y \in G\), and \(\psi , \eta , \chi , \phi :G \rightarrow \mathbb {R}\) are unknown functions.

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与最大函数方程有关的任意群上的广义文采函数方程
摘要 在这篇研究论文中,我们研究了涉及多个(最多四个)未知函数的文采式函数方程的广义化,其最大函数方程为 $$\begin{aligned}\max \{\psi (xy), \psi (xy^{-1})\}&= \psi (x)\eta (y)+\psi (y), \max \{\psi (xy), \psi (xy^{-1})\}&= \psi (x)\eta (y)+\chi (y), \max \{\psi (xy), \psi (xy^{-1})\}&;= \phi (x)\eta (y), \max \{\psi(xy), \psi(xy^{-1})&=\phi(x)\eta(y)+\chi(y), \end{aligned}$$其中 G 是一个任意群,\(x, y 在 G 中), 和 \(\psi , \eta , \chi , \phi:G \rightarrow \mathbb {R}\) 都是未知函数。
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来源期刊
Aequationes Mathematicae
Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
1.70
自引率
12.50%
发文量
62
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.
期刊最新文献
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