关于开区间方程凸解的说明

IF 0.9 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2024-02-24 DOI:10.1007/s00010-024-01038-4

Chaitanya Gopalakrishna

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引用次数: 0

摘要

本说明涉及函数方程 $$\begin{aligned}\lambda _1H_1(f(x))+\lambda _2H_2(f^2(x))+\cdots +\lambda _nH_n(f^n(x))=F(x), \end{aligned}$$这是所谓多项式迭代方程的一般形式。我们利用 Schauder 定点定理研究了该方程在开区间上的非递减凸解（通常解和高阶解）的存在性。这些结果补充了 Trif（Aquat Math，79:315-327，2010 年）针对类多项式迭代方程证明的结果，在更大程度上对其进行了推广。一些例子说明了这些结果的适用性，从而支持了这一论断。

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A note on convex solutions to an equation on open intervals

The note is concerned with the functional equation

$$\begin{aligned} \lambda _1H_1(f(x))+\lambda _2H_2(f^2(x))+\cdots +\lambda _nH_n(f^n(x))=F(x), \end{aligned}$$

which is a generalised form of the so-called polynomial-like iterative equation. We investigate the existence of nondecreasing convex (both usual and higher order) solutions to this equation on open intervals using the Schauder fixed point theorem. The results supplement those proved by Trif (Aquat Math, 79:315–327, 2010) for the polynomial-like iterative equation by generalising them to a greater extent. This assertion is supported by some examples illustrating their applicability.

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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.