Korean Journal of Mathematics

  • 제28권2호
  • /
  • Pages.361-378
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  • 2020
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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DOMAIN OF EULER-TOTIENT MATRIX OPERATOR IN THE SPACE 𝓛p

  • 투고 : 2019.09.30
  • 심사 : 2020.06.17
  • 발행 : 2020.06.30
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초록

The most apparent aspect of the present study is to introduce a new sequence space 𝚽⋆(𝓛p) derived by double Euler-Totient matrix operator. We examine its topological and algebraic properties and give an inclusion relation. In addition to those, the α-, β(bp)- and γ-duals of the space 𝚽⋆(𝓛p) are determined and finally, some 4-dimensional matrix mapping classes related to this space are characterized.

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참고문헌

  1. C.R. Adams, On non-factorable transformations of double sequences, Proc. Natl. Acad. Sci. USA 19 (5) (1933), 564-567. https://doi.org/10.1073/pnas.19.5.564
  2. B. Altay and F. Basar, Some new spaces of double sequences, J. Math. Anal. Appl., 309 (1) (2005), 70-90. https://doi.org/10.1016/j.jmaa.2004.12.020
  3. F. Basar, Summability Theory and Its Applications, Bentham Science Publishers, e-book, Monographs, Istanbul, 2012.
  4. F. Basar and Y. Sever, The space ${\mathcal{L}}_q$ of double sequences, Math. J. Okayama Univ. 51 (2009), 149-157.
  5. J. Boss, Classical and Modern Methods in Summability, Oxford University Press, Newyork, 2000.
  6. R.C. Cooke, Infinite Matrices and Sequence Spaces, Macmillan and Co. Limited, London, 1950.
  7. H. Capan and F. Basar, Some paranormed difference spaces of double sequences, Indian L. Math. 58 (3)(2016), 405-427.
  8. S. Demiriz and O. Duyar, Domain of the Cesaro mean matrix in some paranormed spaces of double sequences, Contemp. Anal. Appl. Math. 3 (2) (2015), 247-262.
  9. H.J. Hamilton, Transformations of multiple sequences, Duke Math. J. 2 (1936), 29-60. https://doi.org/10.1215/S0012-7094-36-00204-1
  10. M. Ilkhan and E. E. Kara, A New Banach Space Defined by Euler Totient Matrix Operator, Operators and Matrices 13 (2) (2019), 527-544.
  11. E.E. Kara, Some topological and geometrical properties of new Banach sequence spaces, Journal of Inequalities and Applications, 2013 (38) (2013), 15 pages.
  12. E.E. Kara and M. Basarir, On some Euler $B^{(m)}$ difference sequence spaces and compact operators, Journal of Mathematical Analysis and Applications, 379 (2011), 499-511. https://doi.org/10.1016/j.jmaa.2011.01.028
  13. E.E. Kara and S. Konca, On some new weighted Euler sequence spaces and compact operators, Mathematical Inequalities and applications 17 (2) (2014), 649-664.
  14. E.E. Kara and M. Ilkhan, On some Banach sequence spaces derived by a new band matrix, British Journal of Mathematics and Computer Science 9 (2) (2015), 141-159. https://doi.org/10.9734/BJMCS/2015/17499
  15. E.E. Kara and M. Ilkhan, Some properties of generalized Fibonacci sequence spaces, Linear and Multilinear Algebra 64 (11) (2016), 2208-2223. https://doi.org/10.1080/03081087.2016.1145626
  16. E. Kovac, On ${\varphi}$ convergence and ${\varphi}$ density, Mathematica Slovaca 55 (2005), 329-351.
  17. F. Moricz, Extensions of the spaces c and $c_0$ from single to double sequences, Acta Math. Hungar. 57 (1991), 129-136. https://doi.org/10.1007/BF01903811
  18. M. Mursaleen, Almost strongly regular matrices and a core theorem for double sequences, J. Math. Anal. Appl. 293 (2) (2004), 523-531. https://doi.org/10.1016/j.jmaa.2004.01.014
  19. M. Mursaleen and F. Basar, Domain of Cesaro mean of order one in some spaces of double sequences, Stud. Sci. Math. Hungar. 51 (3) (2014), 335-356. https://doi.org/10.1556/SScMath.51.2014.3.1287
  20. M. Mursaleen and S. A. Mohiuddine, Convergence Methods for Double Sequences and Applications, Springer, New Delhi, Heidelberg, New York, Dordrecht, London, 2014.
  21. I. Niven, H.S. Zuckerman and H.L. Montgomery, An introduction to the theory of numbers, (5. Edition), Wiley, New York, 1991.
  22. A. Pringsheim, Zur Theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53, 289-321 (1900). https://doi.org/10.1007/BF01448977
  23. G. M. Robison, Divergent double sequences and series, Amer. Math. Soc. Trans, 28 (1926), 50-73. https://doi.org/10.1090/S0002-9947-1926-1501332-5
  24. H.H. Schaefer, Topological Vector Spaces, Graduate Texts in Matematics, Volume 3, 5th printing, 1986.
  25. I. Schoenberg, The integrability of certain functions and related summability methods, The American Monthly, 66 (1959), 361-375. https://doi.org/10.1080/00029890.1959.11989303
  26. M. Stieglitz and H. Tietz, Matrix transformationen von folgenraumen eine ergebnisbersicht, Mathematische Zeitschrift, 154 (1977), 1-16. https://doi.org/10.1007/BF01215107
  27. G. Talebi, Operator norms of four-dimensional Hausdorff matrices on the double Euler sequence spaces, Linear and Multilinear Algebra 65 (11) (2017), 2257-2267. https://doi.org/10.1080/03081087.2016.1267108
  28. O. Tug, Four-dimensional generalized difference matrix and some double sequence spaces, J. Inequal. Appl. 2017, Articla number: 149 (2017).
  29. M.Yesilkayagil and F. Basar, On the Domain of Riesz Mean in the Space ${\mathcal{L}}_s^*$, Filomat, 31 (4) (2017), 925-940. https://doi.org/10.2298/FIL1704925Y
  30. M.Yesilkayagil and F. Basar, Domain of Euler Mean in the Space of Absolutely p-Summable Double Sequences with 0 < p < 1, Anal. Theory Appl. 34 (3) (2018), 241-252. https://doi.org/10.4208/ata.OA-2017-0056
  31. M. Zeltser, Investigation of double sequence spaces by soft and hard analitic methods, Dissertationes Mathematicae Universtaties Tartuensis 25, Tartu University Press, Univ. of Tartu, Faculty of Mathematics and Computer Science, Tartu, 2001.
  32. M. Zeltser, On conservative matrix methods for double sequence spaces, Acta Math. Hung. 95 (3) (2002), 225-242. https://doi.org/10.1023/A:1015636905885
  33. M. Zeltser, M. Mursaleen and S. A. Mohiuddine, On almost conservative matrix mathods for double sequence spaces, Publ. Math. Debrecen, 75 (2009), 387-399.