{"title":"Deferred 𝜎-statistical summability in intuitionistic fuzzy 𝑟-normed linear spaces","authors":"Vijay Kumar, Archana Sharma, Reena Kumari","doi":"10.1515/anly-2023-0088","DOIUrl":null,"url":null,"abstract":"\n <jats:p>In this paper, we define and study three novel summability concepts – strong deferred 𝜎-summability, deferred 𝜎-statistical summability, and 𝜎-statistical summability in intuitionistic fuzzy 𝑟-normed linear spaces (briefly called IF-𝑟-NLS) by using 𝜎-mean.\nWe also provide an example in support of the new notions and uncover some interesting relationships.\nAdditionally, we study deferred 𝜎-statistical summability in the context of two pairs of sequences of positive integers, namely, <jats:inline-formula>\n <jats:alternatives>\n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\n <m:mrow>\n <m:msub>\n <m:mi>α</m:mi>\n <m:mi>n</m:mi>\n </m:msub>\n <m:mo>,</m:mo>\n <m:msub>\n <m:mi>γ</m:mi>\n <m:mi>n</m:mi>\n </m:msub>\n </m:mrow>\n </m:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_anly-2023-0088_ineq_0001.png\" />\n <jats:tex-math>\\alpha_{n},\\gamma_{n}</jats:tex-math>\n </jats:alternatives>\n </jats:inline-formula>, and <jats:inline-formula>\n <jats:alternatives>\n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\n <m:mrow>\n <m:msub>\n <m:mi>u</m:mi>\n <m:mi>n</m:mi>\n </m:msub>\n <m:mo>,</m:mo>\n <m:msub>\n <m:mi>v</m:mi>\n <m:mi>n</m:mi>\n </m:msub>\n </m:mrow>\n </m:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_anly-2023-0088_ineq_0002.png\" />\n <jats:tex-math>u_{n},v_{n}</jats:tex-math>\n </jats:alternatives>\n </jats:inline-formula> satisfying <jats:inline-formula>\n <jats:alternatives>\n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\n <m:mrow>\n <m:msub>\n <m:mi>α</m:mi>\n <m:mi>n</m:mi>\n </m:msub>\n <m:mo>≤</m:mo>\n <m:msub>\n <m:mi>u</m:mi>\n <m:mi>n</m:mi>\n </m:msub>\n <m:mo><</m:mo>\n <m:msub>\n <m:mi>v</m:mi>\n <m:mi>n</m:mi>\n </m:msub>\n <m:mo>≤</m:mo>\n <m:msub>\n <m:mi>γ</m:mi>\n <m:mi>n</m:mi>\n </m:msub>\n </m:mrow>\n </m:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_anly-2023-0088_ineq_0003.png\" />\n <jats:tex-math>\\alpha_{n}\\leq u_{n}<v_{n}\\leq\\gamma_{n}</jats:tex-math>\n </jats:alternatives>\n </jats:inline-formula>.</jats:p>","PeriodicalId":47773,"journal":{"name":"ANALYSIS","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ANALYSIS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/anly-2023-0088","RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"0","JCRName":"PHILOSOPHY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we define and study three novel summability concepts – strong deferred 𝜎-summability, deferred 𝜎-statistical summability, and 𝜎-statistical summability in intuitionistic fuzzy 𝑟-normed linear spaces (briefly called IF-𝑟-NLS) by using 𝜎-mean.
We also provide an example in support of the new notions and uncover some interesting relationships.
Additionally, we study deferred 𝜎-statistical summability in the context of two pairs of sequences of positive integers, namely, αn,γn\alpha_{n},\gamma_{n}, and un,vnu_{n},v_{n} satisfying αn≤un<vn≤γn\alpha_{n}\leq u_{n}.
本文利用𝜎-均值定义并研究了三个新的可求和性概念--强延迟𝜎-可求和性、延迟𝜎-统计可求和性以及直觉模糊𝑟规范线性空间(简称 IF-𝑟-NLS)中的𝜎-统计可求和性。此外,我们还研究了两对正整数序列的延迟𝜎-统计求和性,即 α n , γ n \alpha_{n},\gamma_{n} 和 u n , v n u n \alpha_{n},\gamma_{n} 。 u n , v n u_{n},v_{n} 满足 α n ≤ u n v n ≤ γ n \alpha_{n}\leq u_{n} 。
期刊介绍:
Analysis is the most established and esteemed forum in which to publish short discussions of topics in philosophy. Articles published in Analysis lend themselves to the presentation of cogent but brief arguments for substantive conclusions, and often give rise to discussions which continue over several interchanges. A wide range of topics are covered including: philosophical logic and philosophy of language, metaphysics, epistemology, philosophy of mind, and moral philosophy.