余弦型和正弦型泛函方程的超稳定性

IF 0.1 Q4 MATHEMATICS

Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica Pub Date : 2016-11-29 DOI:10.1515/AUPCSM-2016-0010

F. Lehlou, M. Moussa, A. Roukbi, S. Kabbaj

{"title":"余弦型和正弦型泛函方程的超稳定性","authors":"F. Lehlou, M. Moussa, A. Roukbi, S. Kabbaj","doi":"10.1515/AUPCSM-2016-0010","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we study the superstablity problem of the cosine and sine type functional equations: f(xσ(y)a)+f(xya)=2f(x)f(y) $$f(x\\sigma (y)a) + f(xya) = 2f(x)f(y)$$ and f(xσ(y)a)−f(xya)=2f(x)f(y), $$f(x\\sigma (y)a) - f(xya) = 2f(x)f(y),$$ where f : S → ℂ is a complex valued function; S is a semigroup; σ is an involution of S and a is a fixed element in the center of S.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"44 1","pages":"113 - 121"},"PeriodicalIF":0.1000,"publicationDate":"2016-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"On the superstability of the cosine and sine type functional equations\",\"authors\":\"F. Lehlou, M. Moussa, A. Roukbi, S. Kabbaj\",\"doi\":\"10.1515/AUPCSM-2016-0010\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper, we study the superstablity problem of the cosine and sine type functional equations: f(xσ(y)a)+f(xya)=2f(x)f(y) $$f(x\\\\sigma (y)a) + f(xya) = 2f(x)f(y)$$ and f(xσ(y)a)−f(xya)=2f(x)f(y), $$f(x\\\\sigma (y)a) - f(xya) = 2f(x)f(y),$$ where f : S → ℂ is a complex valued function; S is a semigroup; σ is an involution of S and a is a fixed element in the center of S.\",\"PeriodicalId\":53863,\"journal\":{\"name\":\"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica\",\"volume\":\"44 1\",\"pages\":\"113 - 121\"},\"PeriodicalIF\":0.1000,\"publicationDate\":\"2016-11-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/AUPCSM-2016-0010\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/AUPCSM-2016-0010","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 2

摘要

摘要本文研究了余弦型和正弦型泛函方程的超稳定性问题:f(xσ(y)a)+f(xya)=2f(x)f(y) $$f(x\sigma (y)a) + f(xya) = 2f(x)f(y)$$和f(xσ(y)a)−f(xya)=2f(x)f(y)， $$f(x\sigma (y)a) - f(xya) = 2f(x)f(y),$$其中f: S→是复值函数;S是半群;σ是S的对内化，而a是S中心的一个固定元素。

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

On the superstability of the cosine and sine type functional equations

Abstract In this paper, we study the superstablity problem of the cosine and sine type functional equations: f(xσ(y)a)+f(xya)=2f(x)f(y) $$f(x\sigma (y)a) + f(xya) = 2f(x)f(y)$$ and f(xσ(y)a)−f(xya)=2f(x)f(y), $$f(x\sigma (y)a) - f(xya) = 2f(x)f(y),$$ where f : S → ℂ is a complex valued function; S is a semigroup; σ is an involution of S and a is a fixed element in the center of S.

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

Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica MATHEMATICS-

自引率

11.10%

发文量

审稿时长

15 weeks