Some Remarks Concerning the General Octic Functional Equation

IF 0.7 Q2 MATHEMATICS Muenster Journal of Mathematics Pub Date : 2023-05-16 DOI:10.1155/2023/2930056

Yang-Hi Lee, Jaiok Roh

{"title":"Some Remarks Concerning the General Octic Functional Equation","authors":"Yang-Hi Lee, Jaiok Roh","doi":"10.1155/2023/2930056","DOIUrl":null,"url":null,"abstract":"In this article, we study the stability of various forms for the general octic functional equation \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\n <msubsup>\n <mrow>\n <mstyle displaystyle=\"true\">\n <mo stretchy=\"false\">∑</mo>\n </mstyle>\n </mrow>\n <mrow>\n <mi>i</mi>\n <mo>=</mo>\n <mn>09</mn>\n </mrow>\n <mrow>\n <mn>9</mn>\n </mrow>\n </msubsup>\n <mrow>\n <msub>\n <mrow>\n <mi>C</mi>\n </mrow>\n <mrow>\n <mi>i</mi>\n </mrow>\n </msub>\n <msup>\n <mrow>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mo>−</mo>\n <mn>1</mn>\n </mrow>\n </mfenced>\n </mrow>\n <mrow>\n <mn>9</mn>\n <mo>−</mo>\n <mi>i</mi>\n </mrow>\n </msup>\n <mi>f</mi>\n <mrow>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mi>x</mi>\n <mo>+</mo>\n <mi>i</mi>\n <mi>y</mi>\n </mrow>\n </mfenced>\n </mrow>\n </mrow>\n <mo>=</mo>\n <mn>0</mn>\n <mtext>.</mtext>\n </math>\n We first find a special way of representing a given mapping as the sum of eight mappings. And by using the above representation, we will investigate the hyperstability of the general octic functional equation. Furthermore, we will discuss the Hyers–Ulam–Rassias stability of the general octic functional equation.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Muenster Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2023/2930056","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

Abstract

In this article, we study the stability of various forms for the general octic functional equation

\sum_{i = 09}^{9} C_{i} {(- 1)}^{9 - i} f (x + i y) = 0 .

We first find a special way of representing a given mapping as the sum of eight mappings. And by using the above representation, we will investigate the hyperstability of the general octic functional equation. Furthermore, we will discuss the Hyers–Ulam–Rassias stability of the general octic functional equation.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

关于一般Octic泛函方程的几个注意事项

在本文中，本文研究了广义octic泛函方程∑I = 09 - 9的各种形式的稳定性C i−1 9−1 f x +I y = 0。我们首先找到一种将给定映射表示为八个映射的和的特殊方法。利用上述表述，我们将研究一般octic泛函方程的超稳定性。此外，我们将讨论一般octic泛函方程的Hyers-Ulam-Rassias稳定性。

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分钟内获得全文去求助

来源期刊

Muenster Journal of Mathematics MATHEMATICS-

自引率

0.00%

发文量

G^{}

Weighted Extropy for Concomitants of Upper k-Record Values Based on Huang–Kotz Morgenstern of Bivariate Distribution