The system of mixed type additive-quadratic equations and approximations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-25 DOI:10.1186/s13660-024-03180-8

Abasalt Bodaghi, Hesam Mahzoon, Nasser Mikaeilvand

引用次数: 0

Abstract

In this article, we study the structure of a multiple variable mapping. Indeed, we reduce the system of several mixed additive-quadratic equations defining a multivariable mapping to obtain a single functional equation, say, the multimixed additive-quadratic equation. We also show that such mappings under some conditions can be multi-additive, multi-quadratic and multi-additive-quadratic. Moreover, we establish the Hyers–Ulam stability of the multimixed additive-quadratic equation, using the so-called direct (Hyers) method. Additionally, we present a concrete example (the numerical approximation) regarding the stability of some two variable mappings into real numbers. Applying some characterization results, we indicate two examples for the case that a multimixed additive-quadratic mapping (in the special cases) cannot be stable.

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混合型二次加法方程组及其近似值

在本文中，我们将研究多变量映射的结构。事实上，我们将定义多变量映射的几个混合加-二次方程系简化为一个单一的函数方程，即多混合加-二次方程。我们还证明，在某些条件下，这种映射可以是多正态、多二次态和多正四次态的。此外，我们还利用所谓的直接（Hyers）方法建立了多混合加性-二次方程的 Hyers-Ulam 稳定性。此外，我们还提出了一个具体的例子（数值近似），说明了一些双变量映射到实数的稳定性。应用一些特征化结果，我们指出了两个多变量加二次映射（在特殊情况下）不稳定的例子。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.