References
- 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
- 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
- F. Basar, Summability Theory and Its Applications, Bentham Science Publishers, e-book, Monographs, Istanbul, 2012.
-
F. Basar and Y. Sever, The space
${\mathcal{L}}_q$ of double sequences, Math. J. Okayama Univ. 51 (2009), 149-157. - J. Boss, Classical and Modern Methods in Summability, Oxford University Press, Newyork, 2000.
- R.C. Cooke, Infinite Matrices and Sequence Spaces, Macmillan and Co. Limited, London, 1950.
- H. Capan and F. Basar, Some paranormed difference spaces of double sequences, Indian L. Math. 58 (3)(2016), 405-427.
- 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.
- H.J. Hamilton, Transformations of multiple sequences, Duke Math. J. 2 (1936), 29-60. https://doi.org/10.1215/S0012-7094-36-00204-1
- M. Ilkhan and E. E. Kara, A New Banach Space Defined by Euler Totient Matrix Operator, Operators and Matrices 13 (2) (2019), 527-544.
- E.E. Kara, Some topological and geometrical properties of new Banach sequence spaces, Journal of Inequalities and Applications, 2013 (38) (2013), 15 pages.
-
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 - 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.
- 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
- 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
-
E. Kovac, On
${\varphi}$ convergence and${\varphi}$ density, Mathematica Slovaca 55 (2005), 329-351. -
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 - 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
- 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
- M. Mursaleen and S. A. Mohiuddine, Convergence Methods for Double Sequences and Applications, Springer, New Delhi, Heidelberg, New York, Dordrecht, London, 2014.
- I. Niven, H.S. Zuckerman and H.L. Montgomery, An introduction to the theory of numbers, (5. Edition), Wiley, New York, 1991.
- A. Pringsheim, Zur Theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53, 289-321 (1900). https://doi.org/10.1007/BF01448977
- 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
- H.H. Schaefer, Topological Vector Spaces, Graduate Texts in Matematics, Volume 3, 5th printing, 1986.
- 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
- M. Stieglitz and H. Tietz, Matrix transformationen von folgenraumen eine ergebnisbersicht, Mathematische Zeitschrift, 154 (1977), 1-16. https://doi.org/10.1007/BF01215107
- 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
- O. Tug, Four-dimensional generalized difference matrix and some double sequence spaces, J. Inequal. Appl. 2017, Articla number: 149 (2017).
-
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 - 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
- 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.
- 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
- M. Zeltser, M. Mursaleen and S. A. Mohiuddine, On almost conservative matrix mathods for double sequence spaces, Publ. Math. Debrecen, 75 (2009), 387-399.