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Year 2020, Volume: 8 Issue: 2, 329 - 336, 27.10.2020

Abstract

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

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.
There are 38 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Sezer Erdem 0000-0001-9420-8264

Serkan Demiriz 0000-0002-4662-6020

Publication Date October 27, 2020
Submission Date May 17, 2020
Acceptance Date October 9, 2020
Published in Issue Year 2020 Volume: 8 Issue: 2

Cite

APA Erdem, S., & Demiriz, S. (2020). Almost Convergence and 4-Dimensional Binomial Matrix. Konuralp Journal of Mathematics, 8(2), 329-336.
AMA Erdem S, Demiriz S. Almost Convergence and 4-Dimensional Binomial Matrix. Konuralp J. Math. October 2020;8(2):329-336.
Chicago Erdem, Sezer, and Serkan Demiriz. “Almost Convergence and 4-Dimensional Binomial Matrix”. Konuralp Journal of Mathematics 8, no. 2 (October 2020): 329-36.
EndNote Erdem S, Demiriz S (October 1, 2020) Almost Convergence and 4-Dimensional Binomial Matrix. Konuralp Journal of Mathematics 8 2 329–336.
IEEE S. Erdem and S. Demiriz, “Almost Convergence and 4-Dimensional Binomial Matrix”, Konuralp J. Math., vol. 8, no. 2, pp. 329–336, 2020.
ISNAD Erdem, Sezer - Demiriz, Serkan. “Almost Convergence and 4-Dimensional Binomial Matrix”. Konuralp Journal of Mathematics 8/2 (October 2020), 329-336.
JAMA Erdem S, Demiriz S. Almost Convergence and 4-Dimensional Binomial Matrix. Konuralp J. Math. 2020;8:329–336.
MLA Erdem, Sezer and Serkan Demiriz. “Almost Convergence and 4-Dimensional Binomial Matrix”. Konuralp Journal of Mathematics, vol. 8, no. 2, 2020, pp. 329-36.
Vancouver Erdem S, Demiriz S. Almost Convergence and 4-Dimensional Binomial Matrix. Konuralp J. Math. 2020;8(2):329-36.
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