Year 2020,
Volume: 8 Issue: 2, 329 - 336, 27.10.2020
Sezer Erdem
,
Serkan Demiriz
References
- [1] C.R. Adams, On non-factorable transformations of double sequences, Proc. Natl. Acad. Sci. USA, 19(5) (1933), 564-567.
- [2] B. Altay and F. Bas¸ar, Some new spaces of double sequences, J. Math. Anal. Appl., 309(1) (2005), 70-90.
- [3] M. Arslan and E. Dundar, I-Convergence and I-Cauchy Sequence of Functions in 2 Normed Spaces, Konuralp Journal of Mathematics, 6(1) (2018),
57-62.
- [4] F. Basar and Y. Sever, The space Lq of double sequences, Math. J. Okayama Univ., 51 (2009), 149-157.
- [5] M.C. Bisgin, The binomial sequence spaces which include the spaces `p and `¥ and geometric properties, Journal of Inequalities and Applications
(2016):304.
- [6] M.C. Bis¸gin, The binomial sequence spaces of nonabsolute type, Journal of Inequalities and Applications (2016):309.
- [7] M.C. Bis¸gin, The Binomial Almost Convergent and Null Sequence Spaces, Commun.Fac.Sci.Univ.Ank.Series A1, vol:67,no:1 (2018), 211-224.
- [8] J. Boss, Classical and Modern Methods in Summability, Oxford University Press, Newyork, 2000.
- [9] R.C. Cooke, Infinite Matrices and Sequence Spaces, Macmillan and Co. Limited, London, 1950.
- [10] F. C unjalo, Almost convergence of double sequences-some analogies between measure and category, Math. Maced.5 (2007), 21-24.
- [11] S. Demiriz and O. Duyar, The Weighted Mean Convergence And Weighted Core Of Double Sequences”, Enlightenment Of Pure And Applied
Mathematics, 1(2) (2016), 21-35.
- [12] S. Demiriz and S. Erdem, Domain of Euler-Totient Matrix Operator in the Space Lp, Korean J. Math., 28, No:2 (2020), 361-378.
- [13] E. Dundar, U. Ulusu and B. Aydın, I2-Lacunary Statistical Convergence of Double Sequences of Sets, Konuralp Journal of Mathematics, 5(1) (2017),
1-10.
- [14] E. Dundar and N. Akın, f Asymptotically Is -Equivalence of Real Sequences, Konuralp Journal of Mathematics, vol. 8, no. 1, (2020), 207-2010.
- [15] S. Erdem and S. Demiriz, On the New Generalized Block Difference Sequence Space, Appl. Appl. Math.(AAM), Special Issue 5 (2019), 68-83.
- [16] E. Gulle and U. Ulusu, Quasi-Almost Convergence of Sequences of Sets, Journal of Inequalities and Special Functions, 8(5) (2017), 59-65.
- [17] H. J. Hamilton, Transformations of multiple sequences, Duke Math. J., 2 (1936), 29-60.
- [18] G.G. Lorentz, A contribution to the theory of divergent sequences, Acta Math., 80(1) (1948), 167-190.
- [19] F. Moricz and B.E. Rhoades, Almost convergence of double sequences and strong regularity of summability matrices, Math. Proc. Camb. Philos. Soc.,
104 (1988), 283-294.
- [20] F. Moricz, Extensions of the spaces c and c0 from single to double sequences, Acta Math. Hungar., 57 (1991), 129-136.
- [21] M. Mursaleen, Almost strongly regular matrices and a core theorem for double sequences, J. Math. Anal. Appl., 293(2) (2004), 523-531.
- [22] A. Pringsheim, Zur Theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53, 289-321(1900).
- [23] G. M. Robison, Divergent double sequences and series, Amer. Math. Soc. Trans., 28 (1926), 50-73.
- [24] G. Talebi, Operator norms of four-dimensional Hausdorff matrices on the double Euler sequence spaces, Linear and Multilinear Algebra, 65(11) (2017),
2257-2267.
- [25] O. Tug and F. Basar, Four-Dimensional Generalized Difference Matrix and Some Double Sequence Spaces, AIP Conference Proceedings, vol. 1759.AIP,
New York(2016).
- [26] O. Tug, Four-dimensional generalized difference matrix and some double sequence spaces, J. Inequal. Appl. 2017(1), 149 (2017).
- [27] O. Tug, On almost B-summable double sequence spaces, J. Inequal. Appl. 2018(1):9, 19 pages, (2018).
- [28] O. Tug, On the Characterization of Some Classes of Four-Dimensional Matrices and Almost B-Summable Double Sequences, Journal of Mathematics,
vol.2018, Article ID 1826485, 7 pages, (2018).
- [29] O. Tug, V. Rakocevic and E. Malkowsky, On the Domain of the Four-Dimensional Sequential Band Matrix in Some Double Sequence Spaces,
Mathematics (2020), 8, 789;doi:10.3390/math8050789.
- [30] U. Ulusu and F. Nuray, Lacunary Statistical summability of sequences of sets, Konuralp Journal of Mathematics, 3(2) (2015), 176-184.
- [31] S. Yegul and E. Dundar, I2 Convergence of Double Sequences of Functions in 2 Normed Spaces, Universal Journal of Mathematics and Applications,
2(3) (2019), 130-137.
- [32] M. Yesilkayagil and F. Bas¸ar, Four dimensional dual and dual of some new sort summability methods, Contemp.Anal.Appl.Math.3(1),(2015),pp.13-29.
- [33] M. Yesilkayagil and F. Basar, On the characterization of a class of four dimensional matrices and Steinhaus type theorems, Kragujev. J. Math.
40(1)(2016), pp. 35-45.
- [34] M. Yes¸ilkayagil and F. Basar, Domain of Riesz mean in the space Ls, Filomat, 31(4) (2017), 925-940.
- [35] M. Yes¸ilkayagil and F. Basar, Domain of Euler Mean in the Space of Absolutely p-Summable Double Sequences with 0 < p < 1, Anal. Theory Appl.,
Vol. 34, No. 3(2018), pp. 241-252.
- [36] 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.
- [37] M. Zeltser, On conservative matrix methods for double sequence spaces, Acta Math. Hung., 95(3) (2002), 225-242.
- [38] M. Zeltser, M. Mursaleen and S. A. Mohiuddine, On almost conservative matrix mathods for double sequence spaces, Publ. Math. Debrecen, 75 (2009),
387-399.
Almost Convergence and 4-Dimensional Binomial Matrix
Year 2020,
Volume: 8 Issue: 2, 329 - 336, 27.10.2020
Sezer Erdem
,
Serkan Demiriz
Abstract
In the current paper, we deal with to submit the matrix domains of the 4-dimensional binomial matrix on almost convergent and almost null double sequence spaces. Moreover, we examine some properties and tent to compute the $\alpha-$, $\beta(bp)-$ and $\gamma-$duals. Finally, some new matrix classes are characterized and some significant results are given.
References
- [1] C.R. Adams, On non-factorable transformations of double sequences, Proc. Natl. Acad. Sci. USA, 19(5) (1933), 564-567.
- [2] B. Altay and F. Bas¸ar, Some new spaces of double sequences, J. Math. Anal. Appl., 309(1) (2005), 70-90.
- [3] M. Arslan and E. Dundar, I-Convergence and I-Cauchy Sequence of Functions in 2 Normed Spaces, Konuralp Journal of Mathematics, 6(1) (2018),
57-62.
- [4] F. Basar and Y. Sever, The space Lq of double sequences, Math. J. Okayama Univ., 51 (2009), 149-157.
- [5] M.C. Bisgin, The binomial sequence spaces which include the spaces `p and `¥ and geometric properties, Journal of Inequalities and Applications
(2016):304.
- [6] M.C. Bis¸gin, The binomial sequence spaces of nonabsolute type, Journal of Inequalities and Applications (2016):309.
- [7] M.C. Bis¸gin, The Binomial Almost Convergent and Null Sequence Spaces, Commun.Fac.Sci.Univ.Ank.Series A1, vol:67,no:1 (2018), 211-224.
- [8] J. Boss, Classical and Modern Methods in Summability, Oxford University Press, Newyork, 2000.
- [9] R.C. Cooke, Infinite Matrices and Sequence Spaces, Macmillan and Co. Limited, London, 1950.
- [10] F. C unjalo, Almost convergence of double sequences-some analogies between measure and category, Math. Maced.5 (2007), 21-24.
- [11] S. Demiriz and O. Duyar, The Weighted Mean Convergence And Weighted Core Of Double Sequences”, Enlightenment Of Pure And Applied
Mathematics, 1(2) (2016), 21-35.
- [12] S. Demiriz and S. Erdem, Domain of Euler-Totient Matrix Operator in the Space Lp, Korean J. Math., 28, No:2 (2020), 361-378.
- [13] E. Dundar, U. Ulusu and B. Aydın, I2-Lacunary Statistical Convergence of Double Sequences of Sets, Konuralp Journal of Mathematics, 5(1) (2017),
1-10.
- [14] E. Dundar and N. Akın, f Asymptotically Is -Equivalence of Real Sequences, Konuralp Journal of Mathematics, vol. 8, no. 1, (2020), 207-2010.
- [15] S. Erdem and S. Demiriz, On the New Generalized Block Difference Sequence Space, Appl. Appl. Math.(AAM), Special Issue 5 (2019), 68-83.
- [16] E. Gulle and U. Ulusu, Quasi-Almost Convergence of Sequences of Sets, Journal of Inequalities and Special Functions, 8(5) (2017), 59-65.
- [17] H. J. Hamilton, Transformations of multiple sequences, Duke Math. J., 2 (1936), 29-60.
- [18] G.G. Lorentz, A contribution to the theory of divergent sequences, Acta Math., 80(1) (1948), 167-190.
- [19] F. Moricz and B.E. Rhoades, Almost convergence of double sequences and strong regularity of summability matrices, Math. Proc. Camb. Philos. Soc.,
104 (1988), 283-294.
- [20] F. Moricz, Extensions of the spaces c and c0 from single to double sequences, Acta Math. Hungar., 57 (1991), 129-136.
- [21] M. Mursaleen, Almost strongly regular matrices and a core theorem for double sequences, J. Math. Anal. Appl., 293(2) (2004), 523-531.
- [22] A. Pringsheim, Zur Theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53, 289-321(1900).
- [23] G. M. Robison, Divergent double sequences and series, Amer. Math. Soc. Trans., 28 (1926), 50-73.
- [24] G. Talebi, Operator norms of four-dimensional Hausdorff matrices on the double Euler sequence spaces, Linear and Multilinear Algebra, 65(11) (2017),
2257-2267.
- [25] O. Tug and F. Basar, Four-Dimensional Generalized Difference Matrix and Some Double Sequence Spaces, AIP Conference Proceedings, vol. 1759.AIP,
New York(2016).
- [26] O. Tug, Four-dimensional generalized difference matrix and some double sequence spaces, J. Inequal. Appl. 2017(1), 149 (2017).
- [27] O. Tug, On almost B-summable double sequence spaces, J. Inequal. Appl. 2018(1):9, 19 pages, (2018).
- [28] O. Tug, On the Characterization of Some Classes of Four-Dimensional Matrices and Almost B-Summable Double Sequences, Journal of Mathematics,
vol.2018, Article ID 1826485, 7 pages, (2018).
- [29] O. Tug, V. Rakocevic and E. Malkowsky, On the Domain of the Four-Dimensional Sequential Band Matrix in Some Double Sequence Spaces,
Mathematics (2020), 8, 789;doi:10.3390/math8050789.
- [30] U. Ulusu and F. Nuray, Lacunary Statistical summability of sequences of sets, Konuralp Journal of Mathematics, 3(2) (2015), 176-184.
- [31] S. Yegul and E. Dundar, I2 Convergence of Double Sequences of Functions in 2 Normed Spaces, Universal Journal of Mathematics and Applications,
2(3) (2019), 130-137.
- [32] M. Yesilkayagil and F. Bas¸ar, Four dimensional dual and dual of some new sort summability methods, Contemp.Anal.Appl.Math.3(1),(2015),pp.13-29.
- [33] M. Yesilkayagil and F. Basar, On the characterization of a class of four dimensional matrices and Steinhaus type theorems, Kragujev. J. Math.
40(1)(2016), pp. 35-45.
- [34] M. Yes¸ilkayagil and F. Basar, Domain of Riesz mean in the space Ls, Filomat, 31(4) (2017), 925-940.
- [35] M. Yes¸ilkayagil and F. Basar, Domain of Euler Mean in the Space of Absolutely p-Summable Double Sequences with 0 < p < 1, Anal. Theory Appl.,
Vol. 34, No. 3(2018), pp. 241-252.
- [36] 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.
- [37] M. Zeltser, On conservative matrix methods for double sequence spaces, Acta Math. Hung., 95(3) (2002), 225-242.
- [38] M. Zeltser, M. Mursaleen and S. A. Mohiuddine, On almost conservative matrix mathods for double sequence spaces, Publ. Math. Debrecen, 75 (2009),
387-399.