• 제목/요약/키워드: Absolute summability

검색결과 18건 처리시간 0.017초

무한급수의 총합 가능성과 후세인 보르에 관하여 (On the Summability of Infinite Series and Hüseyin Bor)

  • 이정오
    • 한국수학사학회지
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    • 제30권6호
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    • pp.353-365
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    • 2017

  • In general, there is summability among the mathematical tools that are the criterion for the convergence of infinite series. Many authors have studied on the summability of infinite series, the summability of Fourier series and the summability factors. Especially, $H{\ddot{u}}seyin$ Bor had published his important results on these topics from the beginning of 1980 to the end of 1990. In this paper, we investigate the minor academic genealogy of teachers and pupils from Fourier to $H{\ddot{u}}seyin$ Bor in section 2. We introduce the $H{\ddot{u}}seyin$ Bor's major results of the summability for infinite series from 1983 to 1997 in section 3. In conclusion, we summarize his research characteristics and significance on the summability of infinite series. Also, we present the diagrams of $H{\ddot{u}}seyin$ Bor's minor academic genealogy from Fourier to $H{\ddot{u}}seyin$ Bor and minor research lineage on the summability of infinite series.

  • https://doi.org/10.14477/jhm.2017.30.6.353 인용 PDF KSCI

A NEW PARANORMED SERIES SPACE USING EULER TOTIENT MEANS AND SOME MATRIX TRANSFORMATIONS

  • Gulec, G. Canan Hazar;Ilkhan, Merve
    • Korean Journal of Mathematics
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    • 제28권2호
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    • pp.205-221
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    • 2020

  • Paranormed spaces are important as a generalization of the normed spaces in terms of having more general properties. The aim of this study is to introduce a new paranormed space |𝜙z|(p) over the paranormed space ℓ(p) using Euler totient means, where p = (pk) is a bounded sequence of positive real numbers. Besides this, we investigate topological properties and compute the α-, β-, and γ duals of this paranormed space. Finally, we characterize the classes of infinite matrices (|𝜙z|(p), λ) and (λ, |𝜙z|(p)), where λ is any given sequence space.

  • https://doi.org/10.11568/kjm.2020.28.2.205 인용 PDF KSCI