集合值化的二次函数方程

IF 0.9 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2024-04-21 DOI:10.1007/s00010-024-01067-z

Elham Mohammadi, Abbas Najati, Kazimierz Nikodem

{"title":"集合值化的二次函数方程","authors":"Elham Mohammadi, Abbas Najati, Kazimierz Nikodem","doi":"10.1007/s00010-024-01067-z","DOIUrl":null,"url":null,"abstract":"Consider a real vector space denoted as X, and let cc(Y) represent the collection of all convex and compact subsets of a real Hausdorff topological vector space Y. This paper investigates set-valued solutions of the Pexiderized quadratic functional equation $$\\begin{aligned} f_1(x+y)+f_2(x-y)=f_3(x)+f_4(y), \\end{aligned}$$for unknown functions \$f_1,f_2,f_3,f_4:X\\rightarrow cc(Y)\$. This functional equation incorporates many functional equations including the quadratic, Cauchy’s and Drygas’ equations. A characterization for set-valued solutions of this functional equation is presented in this paper.","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"51 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Set valued pexiderized quadratic functional equation\",\"authors\":\"Elham Mohammadi, Abbas Najati, Kazimierz Nikodem\",\"doi\":\"10.1007/s00010-024-01067-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Consider a real vector space denoted as X, and let cc(Y) represent the collection of all convex and compact subsets of a real Hausdorff topological vector space Y. This paper investigates set-valued solutions of the Pexiderized quadratic functional equation $$\\\\begin{aligned} f_1(x+y)+f_2(x-y)=f_3(x)+f_4(y), \\\\end{aligned}$$for unknown functions \\\$f_1,f_2,f_3,f_4:X\\\\rightarrow cc(Y)\\\$. This functional equation incorporates many functional equations including the quadratic, Cauchy’s and Drygas’ equations. A characterization for set-valued solutions of this functional equation is presented in this paper.\",\"PeriodicalId\":55611,\"journal\":{\"name\":\"Aequationes Mathematicae\",\"volume\":\"51 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-04-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Aequationes Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00010-024-01067-z\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Aequationes Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00010-024-01067-z","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

考虑一个实向量空间，记为 X，让 cc(Y) 表示实 Hausdorff 拓扑向量空间 Y 的所有凸紧凑子集的集合。本文研究了对于未知函数 $f_1,f_2,f_3,f_4:X\rightarrow cc(Y)$ 的 Pexiderized 二次函数方程 $$begin{aligned} f_1(x+y)+f_2(x-y)=f_3(x)+f_4(y), \end{aligned}$$的集合值解。这个函数方程包含了许多函数方程，包括二次方程、柯西方程和德赖加斯方程。本文提出了该函数方程的集值解的特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Set valued pexiderized quadratic functional equation

Consider a real vector space denoted as X, and let cc(Y) represent the collection of all convex and compact subsets of a real Hausdorff topological vector space Y. This paper investigates set-valued solutions of the Pexiderized quadratic functional equation

$$\begin{aligned} f_1(x+y)+f_2(x-y)=f_3(x)+f_4(y), \end{aligned}$$

for unknown functions $f_1,f_2,f_3,f_4:X\rightarrow cc(Y)$. This functional equation incorporates many functional equations including the quadratic, Cauchy’s and Drygas’ equations. A characterization for set-valued solutions of this functional equation is presented in this paper.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.