Have a personal or library account? Click to login
q-Cesàro double sequence space ℒ˜sq$$\tilde {\cal L}_s^q$$ derived by q-analog Cover

q-Cesàro double sequence space ℒ˜sq$$\tilde {\cal L}_s^q$$ derived by q-analog

By: Sezer Erdem and  Serkan Demiriz  
Open Access
|Jul 2023

References

  1. Adams C. Raymond. “On non-factorable transformations of double sequences.” Proc. Natl. Acad. Sci. USA 19, no. 5 (1933): 564-567. Cited on 113.
  2. Aktuğlu, Hüseyin, and Bekar Şerife. “q-Cesáro matrix and q-statistical convergence.” J. Comput. Appl. Math. 235, no. 16 (2011): 4717-4723. Cited on 113.
  3. Altay, Bilâl, and Başar Feyzi. “Some new spaces of double sequences.” J. Math. Anal. Appl. 309, no. 1 (2005): 70-90. Cited on 112.
  4. Başar, Feyzi. “The space 𝓛q of double sequences.” Math. J. Okayama Univ. 51 (2009): 149-157. Cited on 112 and 117.
  5. Başarir, Metin. “On the strong almost convergence of double sequences.” Period. Math. Hungar. 30, no. 3 (1995): 177-181. Cited on 113.
  6. Bekar, Şerife. q-matrix summability methods. Ph.D. Dissertation. Eastern Mediterranean University, 2010. Cited on 113.
  7. Boos, Johann. Classical and Modern Methods in Summability. Oxford Mathematical Monographs. New York: Oxford University Press Inc., 2000. Cited on 117.
  8. Candan, Murat. “Domain of the double sequential band matrix in the spaces of convergent and null sequences.” Adv. Difference Equ. (2014): Art. no. 163. Cited on 113.
  9. Candan, Murat. “A new sequence space isomorphic to the ℓ(p) and compact operators.” J. Math. Comput. Sci. 4, no. 2 (2014): 306-334. Cited on 113.
  10. Candan, Murat. “Some Characteristics of Matrix Operators on Generalized Fibonacci Weighted Difference Sequence Space.” Symmetry 14, no. 7 (2022): Art. no. 1283. Cited on 113.
  11. Cooke, Richard George. Infinite Matrices and Sequence Spaces. London: Macmillan & Co. Limited, 1950. Cited on 113.
  12. Çapan, Hüsamettin, and Başar Feyzi. “On the paranormed space L(t) of double sequences.” Filomat 32, no. 3 (2018): 1043-1053. Cited on 113 and 118.
  13. Çapan, Hüsamettin, and Başar Feyzi. “On some spaces isomorphic to the space of absolutely q-summable double sequences.” Kyungpook Math. J. 58, no. 2 (2018): 271-289. Cited on 113 and 118.
  14. Çinar, Muhammed, and Et Mikail. “q-double Cesaro matrices and q-statistical convergence of double sequences.” Nat. Acad. Sci. Lett. 43, no. 1 (2020): 73-76. Cited on 113.
  15. Demiriz, Serkan, and Duyar Osman. “Domain of difference matrix of order one in some spaces of double sequences.” Gulf J. Math. 3, no. 3 (2015): 85-100. Cited on 113.
  16. Demiriz, Serkan, and Duyar Osman. “Domain of the generalized double Cesàro matrix in some paranormed spaces of double sequences.” Tbilisi Math. J. 10, no. 2 (2017): 43-56. Cited on 113.
  17. Demiriz, Serkan, and Adem Şahin. “q-Cesàro Sequence Spaces Derived by q- analogue.” Adv. Math. Sci. J. 5, no. 2 (2016): 97-110. Cited on 113.
  18. Demiriz, Serkan, and Sezer Erdem. “On the New Double Binomial Sequence Space” Turk. J. Math. Comput. Sci. 12, no. 2 (2020): 101-111. Cited on 113.
  19. Demiriz, Serkan, and Erdem Sezer. “Domain of binomial matrix in some spaces of double sequences.” Punjab Univ. J. Math. (Lahore) 52, no. 11 (Lahore): 65-79. Cited on 113.
  20. Erdem, Sezer, and Demiriz Serkan. “Almost convergence and 4-dimensional binomial matrix.” Konuralp J. Math. 8, no. 2 (2020): 329-336. Cited on 113.
  21. Erdem, Sezer, and Demiriz Serkan. “A new RH-regular matrix derived by Jordan’s function and its domains on some double sequence spaces.” J. Funct. Spaces, to appear. Cited on 113.
  22. Hamilton, Hugh J. “Transformations of multiple sequences.” Duke Math. J. 2, no. 1 (1936): 29-60. Cited on 112.
  23. Hardy, Godfrey Harold. “On the Convergence of Certain Multiple Series.” Proc. London Math. Soc. (2) 1 (1904): 124-128. Cited on 112.
  24. Ilkhan, Merve, Alp Pinar Zengin, and Kara Emrah Evren. “On the spaces of linear operators acting between asymmetric cone normed spaces.” Mediterr. J. Math. 15, no. 3 (2018): Paper No. 136. Cited on 113.
  25. Ilkhan, Merve, and Kara Emrah Evren. “A new Banach space defined by Euler totient matrix operator.” Oper. Matrices 13, no. 2 (2019): 527-544. Cited on 113.
  26. Kac, Victor, and Pokman Cheung. Quantum Calculus. Springer: New York, 2002. Cited on 113.
  27. Móricz, Ferenc, and Rhoades Billy E. “Almost convergence of double sequences and strong regularity of summability matrices.” Math. Proc. Cambridge Philos. Soc. 104, no. 2 (1988): 283-294. Cited on 113.
  28. Mursaleen, Mohammad. “Almost strongly regular matrices and a core theorem for double sequences.” J. Math. Anal. Appl. 293, no. 2 (2004): 523-531. Cited on 113.
  29. Mursaleen, Mohammad, and Başar Feyzi. “Domain of Cesàro mean of order one in some spaces of double sequences.” Studia Sci. Math. Hungar. 51, no. 3 (2014): 335-356. Cited on 113 and 114.
  30. Ng, Peng Nung. “Cesàro sequence spaces of non-absolute type.” Comment. Math. Prace Mat. 20, no. 2 (1977/78): 429-433. Cited on 113.
  31. Pringsheim, Alfred. “Zur Theorie der zweifach unendlichen Zahlenfolgen.” Math. Ann. 53, no. 3 (1900): 289-321. Cited on 112.
  32. Robison, George Merritt. “Divergent double sequences and series.” Trans. Amer. Math. Soc. 28, no. 1 (1926): 50-73. Cited on 112.
  33. Tuğ, Orhan. “Four-dimensional generalized difference matrix and some double sequence spaces.” J. Inequal. Appl. (2017): Paper No. 149. Cited on 113.
  34. Tuğ, Orhan. “On almost B-summable double sequence spaces.” J. Inequal. Appl. (2018): Paper No. 9. Cited on 113.
  35. Tuğ, Orhan. “The spaces of B(r,s,t,u) strongly almost convergent double sequences and matrix transformations.” Bull. Sci. Math. 169 (2021): Paper No. 102989. Cited on 113.
  36. Yaying, Taja, Hazarika Bipan, and Mursaleen Mohammad. “On sequence space derived by the domain of q-Cesàro matrix in ellp space and the associated operator ideal.” J. Math. Anal. Appl. 493, no. 1 (2021): Paper No. 124453. Cited on 113.
  37. Yaying, Taja, Hazarika Bipan, and Mursaleen Mohammad. “On generalized (p, q)- Euler matrix and associated sequence spaces.” J. Funct. Spaces (2021): Art. ID 8899960. Cited on 113.
  38. Yeşilkayagil, Medine, and Başar Feyzi. “On the domain of Riesz mean in the space ℒs*$${\cal L}_s^*$$.” Filomat 31, no. 4 (2017): 925-940. Cited on 113, 117, 118 and 123.
  39. Yeşilkayagil, Medine, and Başar Feyzi. “Domain of Euler mean in the space of absolutely p-summable double sequences with 0 < p < 1.” Anal. Theory Appl. 34, no. 3 (2018): 241-252. Cited on 113.
  40. Zeltser, Maria. Investigation of double sequence spaces by soft and hard analitic methods. Vol. 25 of Dissertationes Mathematicae Universtaties Tartuensis. Tatru: Tartu University Press, 2001. Cited on 112.
  41. Zeltser, Maria. “On conservative matrix methods for double sequence spaces.” Acta Math. Hungar. 95, no. 3 (2002): 225-242. Cited on 112.
  42. Zeltser, Maria, Mursaleen Mohammad, and Mohiuddine Syed Abdul. “On almost conservative matrix methods for double sequence spaces.” Publ. Math. Debrecen 75, no. 3-4 (2009): 387-399. Cited on 113.
DOI: https://doi.org/10.2478/aupcsm-2023-0009 | Journal eISSN: 2300-133X | Journal ISSN: 2081-545X
Language: English
Page range: 111 - 126
Submitted on: Feb 10, 2023
Accepted on: May 9, 2023
Published on: Jul 31, 2023
Published by: Pedagogical University of Cracow
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2023 Sezer Erdem, Serkan Demiriz, published by Pedagogical University of Cracow
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.