双复数的双序列

IF 0.8 4区 综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES
Sujeet Kumar, Binod Chandra Tripathy
{"title":"双复数的双序列","authors":"Sujeet Kumar,&nbsp;Binod Chandra Tripathy","doi":"10.1007/s40010-024-00895-7","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we present the notion of bounded, convergent in Pringsheim sense, null in Pringsheim sense, regular, regular null and absolutely <i>p</i>-sumable double sequences of bi-complex numbers. We have also introduced the concept of repeated limit of the double sequences of bi-complex numbers. We have established that every <i>P</i>-convergent double sequence of bi-complex numbers is not always bounded but regular convergent double sequences of bi-complex numbers is bounded. It is shown that the introduced classes of double sequences of bi-complex numbers are linear spaces. With the help of the Euclidean norm defined on bi-complex numbers, it is shown that among these classes, the bounded classes are Banach spaces. We have established some of their algebraic and topological properties like solidity, monotonic, symmetric and convergence free. Suitable examples have been discussed to support the introduction of the classes of sequences and the properties, those fail to hold.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Double Sequences of Bi-complex Numbers\",\"authors\":\"Sujeet Kumar,&nbsp;Binod Chandra Tripathy\",\"doi\":\"10.1007/s40010-024-00895-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper we present the notion of bounded, convergent in Pringsheim sense, null in Pringsheim sense, regular, regular null and absolutely <i>p</i>-sumable double sequences of bi-complex numbers. We have also introduced the concept of repeated limit of the double sequences of bi-complex numbers. We have established that every <i>P</i>-convergent double sequence of bi-complex numbers is not always bounded but regular convergent double sequences of bi-complex numbers is bounded. It is shown that the introduced classes of double sequences of bi-complex numbers are linear spaces. With the help of the Euclidean norm defined on bi-complex numbers, it is shown that among these classes, the bounded classes are Banach spaces. We have established some of their algebraic and topological properties like solidity, monotonic, symmetric and convergence free. Suitable examples have been discussed to support the introduction of the classes of sequences and the properties, those fail to hold.</p></div>\",\"PeriodicalId\":744,\"journal\":{\"name\":\"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-09-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences\",\"FirstCategoryId\":\"103\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40010-024-00895-7\",\"RegionNum\":4,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","FirstCategoryId":"103","ListUrlMain":"https://link.springer.com/article/10.1007/s40010-024-00895-7","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0

摘要

在本文中,我们提出了有界、普林斯海姆意义上的收敛、普林斯海姆意义上的无效、正则、正则无效和绝对可 p 求和的双复数双序列的概念。我们还引入了双复数双序列重复极限的概念。我们已经确定,每个双复数的 P 收敛双序列并不总是有界的,但双复数的正则收敛双序列是有界的。研究表明,引入的双复数双序列类是线性空间。借助定义在双复数上的欧氏规范,证明在这些类中,有界类是巴拿赫空间。我们建立了它们的一些代数和拓扑性质,如实体性、单调性、对称性和无收敛性。我们还讨论了一些合适的例子,以支持序列类的引入和那些不成立的性质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Double Sequences of Bi-complex Numbers

In this paper we present the notion of bounded, convergent in Pringsheim sense, null in Pringsheim sense, regular, regular null and absolutely p-sumable double sequences of bi-complex numbers. We have also introduced the concept of repeated limit of the double sequences of bi-complex numbers. We have established that every P-convergent double sequence of bi-complex numbers is not always bounded but regular convergent double sequences of bi-complex numbers is bounded. It is shown that the introduced classes of double sequences of bi-complex numbers are linear spaces. With the help of the Euclidean norm defined on bi-complex numbers, it is shown that among these classes, the bounded classes are Banach spaces. We have established some of their algebraic and topological properties like solidity, monotonic, symmetric and convergence free. Suitable examples have been discussed to support the introduction of the classes of sequences and the properties, those fail to hold.

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
CiteScore
2.60
自引率
0.00%
发文量
37
审稿时长
>12 weeks
期刊介绍: To promote research in all the branches of Science & Technology; and disseminate the knowledge and advancements in Science & Technology
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信