Araştırma Makalesi
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Yıl 2025, , 24 - 35, 27.03.2025

Hacer Bilgin Ellidokuzoğlu , Sezer Erdem , Serkan Demiriz

https://doi.org/10.33434/cams.1600828

Öz

Kaynakça

  • [1] G. Bennett, An inequality for Hausdorff means, Houston J. Math., 25(4) (1999), 709–744.
  • [2] A. Wilansky, Summability Through Functional Analysis, Vol. 85, Elsevier, 2000.
  • [3] C. Aydın, F. Başar, On the new sequence spaces which include the spaces c0 and c, Hokkaido Math. J., 33(2) (2004), 383–398.
  • [4] C. Aydın, F. Başar, Some new paranormed sequence spaces, Inf. Sci., 160(1-4) (2004), 27–40.
  • [5] J. Boos, F. P. Cass, Classical and Modern Methods in Summability, Clarendon Press, 2000.
  • [6] S. Demiriz, C. Çakan, On some new paranormed Euler sequence spaces and Euler core, Acta Math. Sin. (Engl. Ser.), 26(7) (2010), 1207–1222.
  • [7] S. Demiriz, S. Erdem, Mersenne matrix operator and its application in p-summable sequence space, Commun. Adv. Math. Sci., 7(1) (2024), 42–55.
  • [8] S. Erdem, S. Demiriz, A. Şahin, Motzkin sequence spaces and Motzkin core, Numer. Funct. Anal. Optim., 45(4) (2024), 1–21.
  • [9] M. Kirişci, F. Başar, Some new sequence spaces derived by the domain of generalized difference matrix, Comput. Math. Appl., 60(5) (2010), 1299–1309.
  • [10] M. Mursaleen, F. Başar, Sequence Spaces: Topics in Modern Summability Theory, CRC Press, 2020.
  • [11] M. Şengönül, F. Başar, Some new Ces`aro sequence spaces of non-absolute type which include, Soochow J. Math., 31(1) (2005), 107–119.
  • [12] R. Chakrabarti, R. Jagannathan, A (p;q)-oscillator realization of two-parameter quantum algebras, J. Phys. A, 24(13) (1991), L711.
  • [13] F. H. Jackson, On q-functions and a certain difference operator, Proc. R. Soc. Edinb., 46(2) (1909), 253–281.
  • [14] V. Kac, P. Cheung, Quantum Calculus, Springer, 2002.
  • [15] T. Yaying, B. Hazarika, M. Mursaleen, Cesaro sequence spaces via (p;q)-calculus and compact matrix operators, J. Anal., 30(4) (2022), 1535–1553.
  • [16] H. Hahn, Über Folgen linearer operationen, Monatsh. Math., 32 (1922), 3–88.
  • [17] K. C. Rao, The Hahn sequence space, Bull. Calcutta Math. Soc., 82 (1990), 72–78.
  • [18] G. Goes, Sequences of bounded variation and sequences of Fourier coefficients II, J. Math. Anal. Appl., 39 (1972), 477–494.
  • [19] E. Malkowsky, V. Rakocevic, O. Tuğ, Compact operators on the Hahn space, Monatsh. Math., 196(3) (2021), 519–551.
  • [20] M. Kirişci, p-Hahn sequence space, Far East J. Math. Sci., 90(1) (2014), 45–63.
  • [21] M. Yeşilkayagil Savaşcı, F. Başar, The Hahn sequence space generated by the Ces`aro mean of order m, Acta Sci. Math. (Szeged), 90 (2024), 53–72.
  • [22] O. Tuğ, E. Malkowsky, B. Hazarika, T. Yaying, On the new generalized Hahn sequence space mathematical equation, Abstr. Appl. Anal., 2022 (2022), Art. ID 6832559.
  • [23] T. Yaying, M. Kirişci, B. Hazarika, O. Tuğ, Domain of q-Ces`aro matrix in Hahn sequence space hd and the space bv of sequences of bounded variation, Filomat, 36(19) (2022), 6427–6441.
  • [24] T. Yaying, B. Hazarika, M. Mursaleen, On some new BK-spaces as the domain of (p;q)-Ces`aro matrix and point spectrum, Iran. J. Sci. Technol., 47(5) (2023), 1565–1574.
  • [25] T. Yaying, B. Hazarika, M. Mursaleen, A study of the q-analogue of the paranormed Ces`aro sequence spaces, Filomat, 38(1) (2024), 99–117.
  • [26] A. M. Jarrah, E. Malkowsky, Ordinary, absolute and strong summability and matrix transformations, Filomat, 17 (2003), 59–78.

The New Hahn Sequence Space via $(p,q)$-Calculus

Yıl 2025, , 24 - 35, 27.03.2025

Hacer Bilgin Ellidokuzoğlu , Sezer Erdem , Serkan Demiriz

https://doi.org/10.33434/cams.1600828

Öz

In this paper, a novel generalized Hahn sequence space, denoted as $h(C(p,q))$, is introduced by utilizing the $(p, q)$-Cesaro matrix. Fundamental properties of this sequence space, such as its completeness and inclusion relations with other well-known sequence spaces, are explored. The duals of this newly constructed sequence space are also determined, providing insights into its structural and functional characteristics. Furthermore, matrix mapping classes of the form $(h(C(p,q)):\mu)$ are characterized for various classical sequence spaces $\mu \in \{c_0, c, \ell_\infty, \ell_1, h\}$, extending the applicability of the proposed space to broader mathematical contexts. The results obtained contribute to the ongoing development of sequence space theory and its applications in functional analysis.

Anahtar Kelimeler

Duals Hahn sequence space Matrix mappings (p,q)-calculus (p,q)-Cesaro matrix

Kaynakça

  • [1] G. Bennett, An inequality for Hausdorff means, Houston J. Math., 25(4) (1999), 709–744.
  • [2] A. Wilansky, Summability Through Functional Analysis, Vol. 85, Elsevier, 2000.
  • [3] C. Aydın, F. Başar, On the new sequence spaces which include the spaces c0 and c, Hokkaido Math. J., 33(2) (2004), 383–398.
  • [4] C. Aydın, F. Başar, Some new paranormed sequence spaces, Inf. Sci., 160(1-4) (2004), 27–40.
  • [5] J. Boos, F. P. Cass, Classical and Modern Methods in Summability, Clarendon Press, 2000.
  • [6] S. Demiriz, C. Çakan, On some new paranormed Euler sequence spaces and Euler core, Acta Math. Sin. (Engl. Ser.), 26(7) (2010), 1207–1222.
  • [7] S. Demiriz, S. Erdem, Mersenne matrix operator and its application in p-summable sequence space, Commun. Adv. Math. Sci., 7(1) (2024), 42–55.
  • [8] S. Erdem, S. Demiriz, A. Şahin, Motzkin sequence spaces and Motzkin core, Numer. Funct. Anal. Optim., 45(4) (2024), 1–21.
  • [9] M. Kirişci, F. Başar, Some new sequence spaces derived by the domain of generalized difference matrix, Comput. Math. Appl., 60(5) (2010), 1299–1309.
  • [10] M. Mursaleen, F. Başar, Sequence Spaces: Topics in Modern Summability Theory, CRC Press, 2020.
  • [11] M. Şengönül, F. Başar, Some new Ces`aro sequence spaces of non-absolute type which include, Soochow J. Math., 31(1) (2005), 107–119.
  • [12] R. Chakrabarti, R. Jagannathan, A (p;q)-oscillator realization of two-parameter quantum algebras, J. Phys. A, 24(13) (1991), L711.
  • [13] F. H. Jackson, On q-functions and a certain difference operator, Proc. R. Soc. Edinb., 46(2) (1909), 253–281.
  • [14] V. Kac, P. Cheung, Quantum Calculus, Springer, 2002.
  • [15] T. Yaying, B. Hazarika, M. Mursaleen, Cesaro sequence spaces via (p;q)-calculus and compact matrix operators, J. Anal., 30(4) (2022), 1535–1553.
  • [16] H. Hahn, Über Folgen linearer operationen, Monatsh. Math., 32 (1922), 3–88.
  • [17] K. C. Rao, The Hahn sequence space, Bull. Calcutta Math. Soc., 82 (1990), 72–78.
  • [18] G. Goes, Sequences of bounded variation and sequences of Fourier coefficients II, J. Math. Anal. Appl., 39 (1972), 477–494.
  • [19] E. Malkowsky, V. Rakocevic, O. Tuğ, Compact operators on the Hahn space, Monatsh. Math., 196(3) (2021), 519–551.
  • [20] M. Kirişci, p-Hahn sequence space, Far East J. Math. Sci., 90(1) (2014), 45–63.
  • [21] M. Yeşilkayagil Savaşcı, F. Başar, The Hahn sequence space generated by the Ces`aro mean of order m, Acta Sci. Math. (Szeged), 90 (2024), 53–72.
  • [22] O. Tuğ, E. Malkowsky, B. Hazarika, T. Yaying, On the new generalized Hahn sequence space mathematical equation, Abstr. Appl. Anal., 2022 (2022), Art. ID 6832559.
  • [23] T. Yaying, M. Kirişci, B. Hazarika, O. Tuğ, Domain of q-Ces`aro matrix in Hahn sequence space hd and the space bv of sequences of bounded variation, Filomat, 36(19) (2022), 6427–6441.
  • [24] T. Yaying, B. Hazarika, M. Mursaleen, On some new BK-spaces as the domain of (p;q)-Ces`aro matrix and point spectrum, Iran. J. Sci. Technol., 47(5) (2023), 1565–1574.
  • [25] T. Yaying, B. Hazarika, M. Mursaleen, A study of the q-analogue of the paranormed Ces`aro sequence spaces, Filomat, 38(1) (2024), 99–117.
  • [26] A. M. Jarrah, E. Malkowsky, Ordinary, absolute and strong summability and matrix transformations, Filomat, 17 (2003), 59–78.
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Temel Matematik (Diğer)
Bölüm Makaleler
Yazarlar

Hacer Bilgin Ellidokuzoğlu 0000-0003-1658-201X

Sezer Erdem 0000-0001-9420-8264

Serkan Demiriz 0000-0002-4662-6020

Erken Görünüm Tarihi 25 Şubat 2025
Yayımlanma Tarihi 27 Mart 2025
Gönderilme Tarihi 13 Aralık 2024
Kabul Tarihi 20 Şubat 2025
Yayımlandığı Sayı Yıl 2025

Kaynak Göster

APA Bilgin Ellidokuzoğlu, H., Erdem, S., & Demiriz, S. (2025). The New Hahn Sequence Space via $(p,q)$-Calculus. Communications in Advanced Mathematical Sciences, 8(1), 24-35. https://doi.org/10.33434/cams.1600828
AMA Bilgin Ellidokuzoğlu H, Erdem S, Demiriz S. The New Hahn Sequence Space via $(p,q)$-Calculus. Communications in Advanced Mathematical Sciences. Mart 2025;8(1):24-35. doi:10.33434/cams.1600828
Chicago Bilgin Ellidokuzoğlu, Hacer, Sezer Erdem, ve Serkan Demiriz. “The New Hahn Sequence Space via $(p,q)$-Calculus”. Communications in Advanced Mathematical Sciences 8, sy. 1 (Mart 2025): 24-35. https://doi.org/10.33434/cams.1600828.
EndNote Bilgin Ellidokuzoğlu H, Erdem S, Demiriz S (01 Mart 2025) The New Hahn Sequence Space via $(p,q)$-Calculus. Communications in Advanced Mathematical Sciences 8 1 24–35.
IEEE H. Bilgin Ellidokuzoğlu, S. Erdem, ve S. Demiriz, “The New Hahn Sequence Space via $(p,q)$-Calculus”, Communications in Advanced Mathematical Sciences, c. 8, sy. 1, ss. 24–35, 2025, doi: 10.33434/cams.1600828.
ISNAD Bilgin Ellidokuzoğlu, Hacer vd. “The New Hahn Sequence Space via $(p,q)$-Calculus”. Communications in Advanced Mathematical Sciences 8/1 (Mart 2025), 24-35. https://doi.org/10.33434/cams.1600828.
JAMA Bilgin Ellidokuzoğlu H, Erdem S, Demiriz S. The New Hahn Sequence Space via $(p,q)$-Calculus. Communications in Advanced Mathematical Sciences. 2025;8:24–35.
MLA Bilgin Ellidokuzoğlu, Hacer vd. “The New Hahn Sequence Space via $(p,q)$-Calculus”. Communications in Advanced Mathematical Sciences, c. 8, sy. 1, 2025, ss. 24-35, doi:10.33434/cams.1600828.
Vancouver Bilgin Ellidokuzoğlu H, Erdem S, Demiriz S. The New Hahn Sequence Space via $(p,q)$-Calculus. Communications in Advanced Mathematical Sciences. 2025;8(1):24-35.

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