{"title":"Some New Cesàro Sequence Spaces of Order α","authors":"Medine Yeşilkayagil Savaşcı, Feyzi Başar","doi":"10.1007/s11253-024-02333-8","DOIUrl":null,"url":null,"abstract":"<p>We introduce the spaces ℓ<sub>∞</sub>(𝒞<sub>α</sub>), <i>f</i>(𝒞<sub>α</sub>), and <i>f</i><sub>0</sub>(𝒞<sub>α</sub>) of Cesàro bounded, Cesàro almost convergent, and Cesàro almost null sequences of order α<i>,</i> respectively. Moreover, we establish some inclusion relations for these spaces and determine the α -, <i>β</i>- and <i>γ</i>-duals of the spaces ℓ<sub>∞</sub> (𝒞<sub>α</sub>) and <i>f</i>(𝒞<sub>α</sub>)<i>.</i> Finally, we characterize the classes of matrix transformations from the space <i>f</i>(𝒞<sub>α</sub>) to any sequence space <i>Y</i> and from any sequence space <i>Y</i> to the space <i>f</i>(𝒞<sub>α</sub>)<i>.</i></p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"11 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ukrainian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11253-024-02333-8","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We introduce the spaces ℓ∞(𝒞α), f(𝒞α), and f0(𝒞α) of Cesàro bounded, Cesàro almost convergent, and Cesàro almost null sequences of order α, respectively. Moreover, we establish some inclusion relations for these spaces and determine the α -, β- and γ-duals of the spaces ℓ∞ (𝒞α) and f(𝒞α). Finally, we characterize the classes of matrix transformations from the space f(𝒞α) to any sequence space Y and from any sequence space Y to the space f(𝒞α).
期刊介绍：
Ukrainian Mathematical Journal publishes articles and brief communications on various areas of pure and applied mathematics and contains sections devoted to scientific information, bibliography, and reviews of current problems. It features contributions from researchers from the Ukrainian Mathematics Institute, the major scientific centers of the Ukraine and other countries.
Ukrainian Mathematical Journal is a translation of the peer-reviewed journal Ukrains’kyi Matematychnyi Zhurnal, a publication of the Institute of Mathematics of the National Academy of Sciences of Ukraine.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
