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\(AK(\vartheta )\)-Property of Double Series Spaces

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Abstract

In the present paper, we show that \(\vartheta \)-convergent double series spaces \({\mathcal {CS}}_\vartheta \) and the series space \(\mathcal {BV}\) of double sequences of bounded variation are BDK-spaces and investigate their \(AK(\vartheta )\)-space property, where \(\vartheta \in \{p,bp,r\}\).

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References

  1. Altay, B., Başar, F.: Some new spaces of double sequences. J. Math. Anal. Appl. 309, 70–90 (2005)

    Article  MathSciNet  Google Scholar 

  2. Başar, F.: Summability Theory and Its Applications. Bentham Science Publishers, e-books, Monographs, İstanbul, (2012)

  3. Başar, F., Sever, Y.: The space \(\cal{L}_{q}\) of double sequences. Math. J. Okayama Univ. 51, 149–157 (2009)

    MathSciNet  MATH  Google Scholar 

  4. Başarır, M.: On the strong almost convergence of double sequences. Period. Math. Hungarica 30(3), 177–181 (1995)

    Article  MathSciNet  Google Scholar 

  5. Boos, J.: Classical and Modern Methods in Summability. Oxford University Press Inc., New York (2000)

    MATH  Google Scholar 

  6. Köthe, G.: Topological Vector Spaces. Springer, New York (1969)

    MATH  Google Scholar 

  7. Milovidov, S.P., Povolotskiĭ, A.I.: Dual spaces of conditional Köthe spaces of double number sequences. Izvestiya Vysshikh Uchebnykh Zavedenĭĭ. Matematika 2, 90–91 (1991)

    Google Scholar 

  8. Móricz, F.: Extensions of the spaces \(c\) and \(c_0\) from single to double sequences. Acta Math. Hungarica 57, 129–136 (1991)

    Article  MathSciNet  Google Scholar 

  9. Mursaleen, M., Mohiuddine, S.A.: Convergence Methods For Double Sequences and Applications. Springer, Heidelberg (2014)

    Book  Google Scholar 

  10. Pringsheim, A.: Zur theorie der zweifach unendlichen Zahlenfolgen. Math. Ann. 53, 289–321 (1900)

    Article  MathSciNet  Google Scholar 

  11. Sagan, H.: Advanced Calculus of Real-Valued Functions of a Real Variable and Vector-Valued Functions of a Vector Variable. Houghton Mifflin Company, Boston (1974)

    MATH  Google Scholar 

  12. Sever, Y.: On double sequence and double series. Master Thesis, İnönü University, Malatya, Turkey, (2006)

  13. Yeşilkayagil, M., Başar, F.: Some topological properties of the spaces of almost null and almost convergent double sequences. Turkish J. Math. 40(3), 624–630 (2016)

    Article  MathSciNet  Google Scholar 

  14. Zeltser, M.: Investigation of Double Sequence Spaces By Soft and Hard Analitical Methods. Dissertationes Mathematicae Universtaties Tartuensis 25, Tartu University Press, Univ. of Tartu, Faculty of Mathematics and Computer Science, Tartu, (2001)

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Acknowledgements

We are indebted to the referees for helpful suggestions and insights concerning the presentation of this paper.

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Author notes

  1. Feyzi Başar

    Present address: , Dumlupınar Mah. Hızırbey Cad. Binyıl Apt. No: 179-181, D: 1, 34730, Kadıköy/İstanbul, Turkey

Authors and Affiliations

  1. School of Applied Sciences, Uşak University, 1 Eylül Campus, 64200, Uşak, Turkey

    Medıne Yeşılkayagıl

  2. Department of Primary Mathematics Teacher Education, İnönü University, 44280, Malatya, Turkey

    Feyzi Başar

Authors
  1. Medıne Yeşılkayagıl
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  2. Feyzi Başar
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Correspondence to Medıne Yeşılkayagıl.

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Communicated by Rosihan M. Ali.

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Yeşılkayagıl, M., Başar, F. \(AK(\vartheta )\)-Property of Double Series Spaces. Bull. Malays. Math. Sci. Soc. 44, 881–889 (2021). https://doi.org/10.1007/s40840-020-00982-z

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  • DOI: https://doi.org/10.1007/s40840-020-00982-z

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