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Year 2021, Volume: 4 Issue: 4, 271 - 279, 01.12.2021

Sezer Erdem Serkan Demiriz

https://doi.org/10.33401/fujma.987981
Cited By: 2

Abstract

References

  • [1] S. Demiriz, S. Erdem, On the new double binomial sequence space, Turk. J. Math. Comput. Sci., 12(2) (2020) 101–111.
  • [2] S. Demiriz, S. Erdem, Domain of binomial matrix in some spaces of double sequences, Punjab Uni. J. Math., 52(11) (2020), 65-79.
  • [3] S. Erdem, S. Demiriz, Almost convergence and 4-dimensional binomial matrix, Konuralp J. Math., 8(2) (2020), 329-336.
  • [4] M. Zeltser, On conservative matrix methods for double sequence spaces, Acta Math. Hung., 95(3) (2002), 225-242.
  • [5] M. Zeltser, Investigation of double sequence spaces by soft and hard analytic methods, Ph.D. Thesis, Uni., Tartu, 2001.
  • [6] B. Altay, F. Başar, Some new spaces of double sequences, J. Math. Anal. Appl., 309(1) (2005), 70-90.
  • [7] G. Talebi, Operator norms of four-dimensional Hausdorff matrices on the double Euler sequence spaces, Linear and Multilinear Algebra, 65(11) (2017), 2257-2267.
  • [8] M.Yeşilkayagil, F. Başar, 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.
  • [9] O. Tuğ, Four-dimensional generalized difference matrix and some double sequence spaces, J. Inequal. Appl., 2017(1) (2017), 1-22.
  • [10] O. Tuğ, On almost B-summable double sequence spaces, J. Inequal. Appl., 2018(1) (2018), 1-19.
  • [11] O. Tuğ, The spaces of B(r; s; t;u) strongly almost convergent double sequences and matrix transformations, Bull. Sci. Math., 169(2021), 102989.
  • [12] M.C. Bişgin, The binomial sequence spaces which include the spaces `p and `¥ and geometric properties, J. Inequal. Appl., 2016 (2016), 304.
  • [13] M.C. Bişgin, The binomial sequence spaces of nonabsolute type, J. Inequal. Appl., 2016(1) (2016), 1-16.
  • [14] M.C. Bişgin, The binomial almost convergent and null sequence spaces, Commun. Fac. Sci. Uni. Ank. Series A1, 67(1) (2018), 211-224.
  • [15] F. Moricz, B.E. Rhoades, Almost convergence of double sequences and strong regularity of summability matrices, Math. Proc. Camb. Philos. Soc., 104 (1988), 283-294.
  • [16] M. Başarır, On the strong almost convergence of double sequences, Period. Math. Hung., 30(3) (1995), 177–181.
  • [17] C.R. Adams, On non-factorable transformations of double sequences, Proc. Natl. Acad. Sci. USA, 19(5) (1933), 564-567.
  • [18] P.Z. Alp, E.E. Kara, The new class Lz;p;E of s􀀀 type operators, AIMS Math., 4(3) (2019), 779-791.
  • [19] F. Başar, Y. Sever, The space Lq of double sequences, Math. J. Okayama Uni., 51 (2009), 149-157.
  • [20] R.C. Cooke, Infinite Matrices and Sequence Spaces, Macmillan and Co. Limited, London, 1950.
  • [21] S. Erdem, S. Demiriz, A new RH-regular matrix derived by Jordan’s function and its domains on some double sequence spaces, J. Function Spaces, 2021 (2021), Article ID 5594751, 9 pages.
  • [22] H. J. Hamilton, Transformations of multiple sequences, Duke Math. J., 2 (1936), 29-60.
  • [23] M. İlkhan, M. A. Bayrakdar, A study on matrix domain of Riesz-Euler totient matrix in the space of p-absolutely summable sequences, Com. Adv. Math. Sci., 4(1) (2021), 14-25.
  • [24] V.A. Khan, U. Tuba, On paranormed Ideal convergent sequence spaces defined by Jordan totient function, J. Inequal. Appl., 2021(1) (2021), 1-16, https://doi.org/10.1186/s13660-021-02634-7.
  • [25] M. Kirisci, F. Başar, Some new sequence spaces derived by the domain of generalized difference matrix, Computers and Mathematics with Applications, 60(5) (2010), 1299–1309.
  • [26] M. Mursaleen, Almost strongly regular matrices and a core theorem for double sequences, J. Math. Anal. Appl., 293(2) (2004), 523-531.
  • [27] A.K. Noman, E.S. Al Yari, New general results on matrix domains of triangles in sequence spaces, Albaydha Uni. J., 3(2) (2021), 57-72.
  • [28] F. Nuray, U. Ulusu, E. Dündar, Ces`aro summability of double sequences of sets, General Mathematics Notes, 25(1) (2014), 8–18.
  • [29] F. Nuray, U. Ulusu, Lacunary invariant statistical convergence of double sequences of sets, Creative Math. and Info., 28(2) (2019), 143–150.
  • [30] F. Nuray, E. Dündar, U. Ulusu, Wijsman statistical convergence of double sequences of set, Iranian J. Math. Sci. Info., 16(1) (2021), 55–64.
  • [31] A. Pringsheim, Zur Theorie der zweifach unendlichen Zahlenfolgen, Math. Ann., 53 (1900), 289-321.
  • [32] G. M. Robison, Divergent double sequences and series, Amer. Math. Soc. Trans., 28 (1926), 50-73.
  • [33] O. Tuğ, V. Rakocevic, E. Malkowsky, On the domain of the four-dimensional sequential band matrix in some double sequence Spaces, Mathematics, 8(5)(2020), 789.
  • [34] O. Tuğ, The spaces of B(r; s; t;u) strongly almost convergent double sequences and matrix transformations, Bull. Sci. Math., 169 (2021), 102989.
  • [35] T. Yaying, B. Hazarika, On sequence spaces generated by binomial difference operator of fractional order, Math. Slovaca, 69(4) (2019), 901–918.
  • [36] M.Yeşilkayagil, F. Başar, Some topological properties of the spaces of almost null and almost convergent double sequences, Turk. J. Math., 40(3) (2016), 624-630.
  • [37] M.Yeşilkayagil, F. Başar, On the characterization of a class of four-dimensional matrices and Steinhaus type theorems, Kragujevac J. Math., 40(1)(2016), 35-45.
  • [38] M.Yeşilkayagil, F. Başar, Domain of Riesz mean in the space Lp, Filomat, 31(4) (2017), 925-940.
  • [39] M. Zeltser, M. Mursaleen, S. A. Mohiuddine, On almost conservative matrix methods for double sequence spaces, Publ. Math. Debrecen, 75 (2009), 387-399.

A Study on Strongly Almost Convergent and Strongly Almost Null Binomial Double Sequence Spaces

Year 2021, Volume: 4 Issue: 4, 271 - 279, 01.12.2021

Sezer Erdem Serkan Demiriz

https://doi.org/10.33401/fujma.987981
Cited By: 2

Abstract

The 4 dimensional (4d) binomial matrix and its domains on the classical double sequence spaces $\mathcal{L}_{p}$, $\mathcal{M}_{u}$, $\mathcal{C}_{P}$, $\mathcal{C}_{bP}$, $\mathcal{C}_{r}$, $\mathcal{C}_{f}$ and $\mathcal{C}_{f_0}$ have been described and examined by Demiriz and Erdem in the papers \cite{e.d.2}-\cite{e.d.3}. In this article, we describe two double sequence spaces with the aid of the aforementioned matrix and study some properties of these. After giving inclusion relations, we compute $\alpha-$, $\beta(bp)-$ and $\gamma-$duals and give some new matrix classes related them.

Keywords

4d binomial matrix Double sequence space Duals Matrix transformations RH regularity

References

  • [1] S. Demiriz, S. Erdem, On the new double binomial sequence space, Turk. J. Math. Comput. Sci., 12(2) (2020) 101–111.
  • [2] S. Demiriz, S. Erdem, Domain of binomial matrix in some spaces of double sequences, Punjab Uni. J. Math., 52(11) (2020), 65-79.
  • [3] S. Erdem, S. Demiriz, Almost convergence and 4-dimensional binomial matrix, Konuralp J. Math., 8(2) (2020), 329-336.
  • [4] M. Zeltser, On conservative matrix methods for double sequence spaces, Acta Math. Hung., 95(3) (2002), 225-242.
  • [5] M. Zeltser, Investigation of double sequence spaces by soft and hard analytic methods, Ph.D. Thesis, Uni., Tartu, 2001.
  • [6] B. Altay, F. Başar, Some new spaces of double sequences, J. Math. Anal. Appl., 309(1) (2005), 70-90.
  • [7] G. Talebi, Operator norms of four-dimensional Hausdorff matrices on the double Euler sequence spaces, Linear and Multilinear Algebra, 65(11) (2017), 2257-2267.
  • [8] M.Yeşilkayagil, F. Başar, 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.
  • [9] O. Tuğ, Four-dimensional generalized difference matrix and some double sequence spaces, J. Inequal. Appl., 2017(1) (2017), 1-22.
  • [10] O. Tuğ, On almost B-summable double sequence spaces, J. Inequal. Appl., 2018(1) (2018), 1-19.
  • [11] O. Tuğ, The spaces of B(r; s; t;u) strongly almost convergent double sequences and matrix transformations, Bull. Sci. Math., 169(2021), 102989.
  • [12] M.C. Bişgin, The binomial sequence spaces which include the spaces `p and `¥ and geometric properties, J. Inequal. Appl., 2016 (2016), 304.
  • [13] M.C. Bişgin, The binomial sequence spaces of nonabsolute type, J. Inequal. Appl., 2016(1) (2016), 1-16.
  • [14] M.C. Bişgin, The binomial almost convergent and null sequence spaces, Commun. Fac. Sci. Uni. Ank. Series A1, 67(1) (2018), 211-224.
  • [15] F. Moricz, B.E. Rhoades, Almost convergence of double sequences and strong regularity of summability matrices, Math. Proc. Camb. Philos. Soc., 104 (1988), 283-294.
  • [16] M. Başarır, On the strong almost convergence of double sequences, Period. Math. Hung., 30(3) (1995), 177–181.
  • [17] C.R. Adams, On non-factorable transformations of double sequences, Proc. Natl. Acad. Sci. USA, 19(5) (1933), 564-567.
  • [18] P.Z. Alp, E.E. Kara, The new class Lz;p;E of s􀀀 type operators, AIMS Math., 4(3) (2019), 779-791.
  • [19] F. Başar, Y. Sever, The space Lq of double sequences, Math. J. Okayama Uni., 51 (2009), 149-157.
  • [20] R.C. Cooke, Infinite Matrices and Sequence Spaces, Macmillan and Co. Limited, London, 1950.
  • [21] S. Erdem, S. Demiriz, A new RH-regular matrix derived by Jordan’s function and its domains on some double sequence spaces, J. Function Spaces, 2021 (2021), Article ID 5594751, 9 pages.
  • [22] H. J. Hamilton, Transformations of multiple sequences, Duke Math. J., 2 (1936), 29-60.
  • [23] M. İlkhan, M. A. Bayrakdar, A study on matrix domain of Riesz-Euler totient matrix in the space of p-absolutely summable sequences, Com. Adv. Math. Sci., 4(1) (2021), 14-25.
  • [24] V.A. Khan, U. Tuba, On paranormed Ideal convergent sequence spaces defined by Jordan totient function, J. Inequal. Appl., 2021(1) (2021), 1-16, https://doi.org/10.1186/s13660-021-02634-7.
  • [25] M. Kirisci, F. Başar, Some new sequence spaces derived by the domain of generalized difference matrix, Computers and Mathematics with Applications, 60(5) (2010), 1299–1309.
  • [26] M. Mursaleen, Almost strongly regular matrices and a core theorem for double sequences, J. Math. Anal. Appl., 293(2) (2004), 523-531.
  • [27] A.K. Noman, E.S. Al Yari, New general results on matrix domains of triangles in sequence spaces, Albaydha Uni. J., 3(2) (2021), 57-72.
  • [28] F. Nuray, U. Ulusu, E. Dündar, Ces`aro summability of double sequences of sets, General Mathematics Notes, 25(1) (2014), 8–18.
  • [29] F. Nuray, U. Ulusu, Lacunary invariant statistical convergence of double sequences of sets, Creative Math. and Info., 28(2) (2019), 143–150.
  • [30] F. Nuray, E. Dündar, U. Ulusu, Wijsman statistical convergence of double sequences of set, Iranian J. Math. Sci. Info., 16(1) (2021), 55–64.
  • [31] A. Pringsheim, Zur Theorie der zweifach unendlichen Zahlenfolgen, Math. Ann., 53 (1900), 289-321.
  • [32] G. M. Robison, Divergent double sequences and series, Amer. Math. Soc. Trans., 28 (1926), 50-73.
  • [33] O. Tuğ, V. Rakocevic, E. Malkowsky, On the domain of the four-dimensional sequential band matrix in some double sequence Spaces, Mathematics, 8(5)(2020), 789.
  • [34] O. Tuğ, The spaces of B(r; s; t;u) strongly almost convergent double sequences and matrix transformations, Bull. Sci. Math., 169 (2021), 102989.
  • [35] T. Yaying, B. Hazarika, On sequence spaces generated by binomial difference operator of fractional order, Math. Slovaca, 69(4) (2019), 901–918.
  • [36] M.Yeşilkayagil, F. Başar, Some topological properties of the spaces of almost null and almost convergent double sequences, Turk. J. Math., 40(3) (2016), 624-630.
  • [37] M.Yeşilkayagil, F. Başar, On the characterization of a class of four-dimensional matrices and Steinhaus type theorems, Kragujevac J. Math., 40(1)(2016), 35-45.
  • [38] M.Yeşilkayagil, F. Başar, Domain of Riesz mean in the space Lp, Filomat, 31(4) (2017), 925-940.
  • [39] M. Zeltser, M. Mursaleen, S. A. Mohiuddine, On almost conservative matrix methods for double sequence spaces, Publ. Math. Debrecen, 75 (2009), 387-399.
There are 39 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 December 1, 2021
Submission Date August 27, 2021
Acceptance Date November 12, 2021
Published in Issue Year 2021 Volume: 4 Issue: 4

Cite

APA Erdem, S., & Demiriz, S. (2021). A Study on Strongly Almost Convergent and Strongly Almost Null Binomial Double Sequence Spaces. Fundamental Journal of Mathematics and Applications, 4(4), 271-279. https://doi.org/10.33401/fujma.987981
AMA Erdem S, Demiriz S. A Study on Strongly Almost Convergent and Strongly Almost Null Binomial Double Sequence Spaces. FUJMA. December 2021;4(4):271-279. doi:10.33401/fujma.987981
Chicago Erdem, Sezer, and Serkan Demiriz. “A Study on Strongly Almost Convergent and Strongly Almost Null Binomial Double Sequence Spaces”. Fundamental Journal of Mathematics and Applications 4, no. 4 (December 2021): 271-79. https://doi.org/10.33401/fujma.987981.
EndNote Erdem S, Demiriz S (December 1, 2021) A Study on Strongly Almost Convergent and Strongly Almost Null Binomial Double Sequence Spaces. Fundamental Journal of Mathematics and Applications 4 4 271–279.
IEEE S. Erdem and S. Demiriz, “A Study on Strongly Almost Convergent and Strongly Almost Null Binomial Double Sequence Spaces”, FUJMA, vol. 4, no. 4, pp. 271–279, 2021, doi: 10.33401/fujma.987981.
ISNAD Erdem, Sezer - Demiriz, Serkan. “A Study on Strongly Almost Convergent and Strongly Almost Null Binomial Double Sequence Spaces”. Fundamental Journal of Mathematics and Applications 4/4 (December 2021), 271-279. https://doi.org/10.33401/fujma.987981.
JAMA Erdem S, Demiriz S. A Study on Strongly Almost Convergent and Strongly Almost Null Binomial Double Sequence Spaces. FUJMA. 2021;4:271–279.
MLA Erdem, Sezer and Serkan Demiriz. “A Study on Strongly Almost Convergent and Strongly Almost Null Binomial Double Sequence Spaces”. Fundamental Journal of Mathematics and Applications, vol. 4, no. 4, 2021, pp. 271-9, doi:10.33401/fujma.987981.
Vancouver Erdem S, Demiriz S. A Study on Strongly Almost Convergent and Strongly Almost Null Binomial Double Sequence Spaces. FUJMA. 2021;4(4):271-9.

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