Monotonic solutions of a composite functional equation

IF 0.9 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2026-10-05 DOI:10.1007/s00010-026-01330-5

Soichi Ikeda

引用次数: 0

Abstract

Chao first considered the composite functional equation

$$\begin{aligned} f(x + 2f(y)) = f(x) + y + f(y) \quad (x, y \in \mathbb {R}), \end{aligned}$$

where $f: \mathbb {R} \rightarrow \mathbb {R}$. This equation was studied by several mathematicians. In this paper, we study the monotonic solutions of the composite functional equation

$$\begin{aligned} f(xyf(y)) = f(x) y f(y) \quad (x, y \in \mathbb {R}), \end{aligned}$$

where $f: \mathbb {R} \rightarrow \mathbb {R}$. This equation is similar to Chao’s equation.

查看原文本刊更多论文

复合泛函方程的单调解

Chao首先考虑了复合泛函方程$$\begin{aligned} f(x + 2f(y)) = f(x) + y + f(y) \quad (x, y \in \mathbb {R}), \end{aligned}$$，其中$f: \mathbb {R} \rightarrow \mathbb {R}$。几个数学家研究过这个方程。本文研究了复合泛函方程$$\begin{aligned} f(xyf(y)) = f(x) y f(y) \quad (x, y \in \mathbb {R}), \end{aligned}$$的单调解，其中$f: \mathbb {R} \rightarrow \mathbb {R}$。这个方程与赵的方程相似。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.