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New Sequence Spaces Derived From the Composition of Integrated and Differentiated Spaces and Binomial Matrix

Year 2024, Volume: 16 Issue: 2, 373 - 385, 31.12.2024
https://doi.org/10.47000/tjmcs.1321967

Abstract

In this article, we construct new sequence spaces by combining the integrated and differentiated sequence spaces with the binomial matrix. We first construct the properties of these new sequence spaces and we examine some inclusion relations. Furthermore, we determine $\alpha-$, $\beta-$ and $\gamma-$ duals of the integrated and differentiated sequence spaces separately and provide proofs for some of them. Additionally, we characterize some matrix classes associated with these new sequence spaces, along with the obtained results. Finally, we investigate some geometric properties of new integrated sequence spaces.

References

  • Başar, F., Altay, B., On the space of sequences of p-bounded variation and related matrix mappings, Ukrainian Mathematical Journal, 55(2003), 136–147.
  • Bisgin, M.C., The binomial sequence spaces of nonabsolute type, Journal Of Inequalities And Applications, 2016(2016), 309.
  • Bisgin, M.C., The binomial sequence spaces which include the spaces ℓp and ℓ∞ and geometric properties, Journal Of Inequalities And Applications, 2016(2016), 304.
  • Bisgin, M.C., The binomial almost convergent and null sequence spaces, Communications Faculty Of Sciences University Of Ankara-Series A1 Mathematics And Statıstics , 67(1)(2018), 211–224.
  • Bisgin, M.C., Matrix transformations and compact operators on the binomial sequence spaces, Korean Journal Of Mathematics , 27(4)(2019), 949–968.
  • Bişgin, M.C., Binom ve üçlü band matrislerinin kompozisyonu ile türetilen bazı yeni dizi uzayları, 12. Ankara Matematik Günleri , 25-26 Mayıs (2017), Ankara.
  • Choudhary, B., Nanda, S., Functional Analysis with Applications, John Wiley & Sons, 1989.
  • Clarkson, J.A., Uniformly convex spaces, Transactions of the American Mathematical Society, 40(3)(1936), 396–414.
  • Day, M. M., Uniform convexity in factor and conjugate spaces, Annals of Mathematics, 45(2)(1944), 375–385.
  • Garcia-Falset, J., Stability and fixed points for nonexpansive mappings, Houston Journal of Mathematics, 20(3)(1994), 495–506.
  • Garcia-Falset, J., The fixed point property in Banach spaces with the NUS-property, Journal of Mathematical Analysis and Applications, 215(2) (1997), 532–542.
  • Goes, G., Goes, S., Sequences of bounded variation and sequences of Fourier coefficients. I., Math. Z., 118(1970), 93–102.
  • Gurari, V.I., On differential properties of the convexity moduli of Banach spaces, Matematicheskie Issledovaniya, 2(1967), 141–148.
  • Kirişci, M., Integrated and differentiated sequence spaces, Journal Nonlinear Analysis and Application , 2015(1)(2015), 2–16.
  • Kirişci, M., Reisz type integrated and differentiated sequence spaces, Bulletın Of Mathematıcal Analysıs And Applıcatıons , 7(2) (2015), 14–27.
  • Kirişci, M., Integrated and differentiated sequence spaces and weighted mean, Journal of Advances in Mathematics and Computer Science , 29(1)(2018), 1–11.
  • Meng, J., Song, M., On some binomial difference sequence spaces, Kyungpook Mathematical Journal, 57(4)(2017), 631–640.
  • Opial, Z., Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bulletin of the American Mathematical Society, 73(1967), 591–597.
  • Sönmez, A., Some new sequence spaces derived by the composition of binomial matrıx and double band matrix, Journal of Applied Analysis And Computation , 9(1)(2019), 231–244.
  • Stieglitz, M., Tietz, H., Matrixtransformationen von Folgenr¨aumen Eine Ergebnis¨ubersicht, Mathematische Zeitschrift, 154(1977), 1–16.
  • Topal, K., New sequence spaces derived by the composition of binomial and quadruple band matrices, (Under Review).
  • Wilansky, A., Summability Through Functional Analysis, North-Holland Mathematics Studies , Amsterdam, 1984.
Year 2024, Volume: 16 Issue: 2, 373 - 385, 31.12.2024
https://doi.org/10.47000/tjmcs.1321967

Abstract

References

  • Başar, F., Altay, B., On the space of sequences of p-bounded variation and related matrix mappings, Ukrainian Mathematical Journal, 55(2003), 136–147.
  • Bisgin, M.C., The binomial sequence spaces of nonabsolute type, Journal Of Inequalities And Applications, 2016(2016), 309.
  • Bisgin, M.C., The binomial sequence spaces which include the spaces ℓp and ℓ∞ and geometric properties, Journal Of Inequalities And Applications, 2016(2016), 304.
  • Bisgin, M.C., The binomial almost convergent and null sequence spaces, Communications Faculty Of Sciences University Of Ankara-Series A1 Mathematics And Statıstics , 67(1)(2018), 211–224.
  • Bisgin, M.C., Matrix transformations and compact operators on the binomial sequence spaces, Korean Journal Of Mathematics , 27(4)(2019), 949–968.
  • Bişgin, M.C., Binom ve üçlü band matrislerinin kompozisyonu ile türetilen bazı yeni dizi uzayları, 12. Ankara Matematik Günleri , 25-26 Mayıs (2017), Ankara.
  • Choudhary, B., Nanda, S., Functional Analysis with Applications, John Wiley & Sons, 1989.
  • Clarkson, J.A., Uniformly convex spaces, Transactions of the American Mathematical Society, 40(3)(1936), 396–414.
  • Day, M. M., Uniform convexity in factor and conjugate spaces, Annals of Mathematics, 45(2)(1944), 375–385.
  • Garcia-Falset, J., Stability and fixed points for nonexpansive mappings, Houston Journal of Mathematics, 20(3)(1994), 495–506.
  • Garcia-Falset, J., The fixed point property in Banach spaces with the NUS-property, Journal of Mathematical Analysis and Applications, 215(2) (1997), 532–542.
  • Goes, G., Goes, S., Sequences of bounded variation and sequences of Fourier coefficients. I., Math. Z., 118(1970), 93–102.
  • Gurari, V.I., On differential properties of the convexity moduli of Banach spaces, Matematicheskie Issledovaniya, 2(1967), 141–148.
  • Kirişci, M., Integrated and differentiated sequence spaces, Journal Nonlinear Analysis and Application , 2015(1)(2015), 2–16.
  • Kirişci, M., Reisz type integrated and differentiated sequence spaces, Bulletın Of Mathematıcal Analysıs And Applıcatıons , 7(2) (2015), 14–27.
  • Kirişci, M., Integrated and differentiated sequence spaces and weighted mean, Journal of Advances in Mathematics and Computer Science , 29(1)(2018), 1–11.
  • Meng, J., Song, M., On some binomial difference sequence spaces, Kyungpook Mathematical Journal, 57(4)(2017), 631–640.
  • Opial, Z., Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bulletin of the American Mathematical Society, 73(1967), 591–597.
  • Sönmez, A., Some new sequence spaces derived by the composition of binomial matrıx and double band matrix, Journal of Applied Analysis And Computation , 9(1)(2019), 231–244.
  • Stieglitz, M., Tietz, H., Matrixtransformationen von Folgenr¨aumen Eine Ergebnis¨ubersicht, Mathematische Zeitschrift, 154(1977), 1–16.
  • Topal, K., New sequence spaces derived by the composition of binomial and quadruple band matrices, (Under Review).
  • Wilansky, A., Summability Through Functional Analysis, North-Holland Mathematics Studies , Amsterdam, 1984.
There are 22 citations in total.

Details

Primary Language English
Subjects Operator Algebras and Functional Analysis
Journal Section Articles
Authors

Kübra Topal 0000-0001-9267-5627

Publication Date December 31, 2024
Published in Issue Year 2024 Volume: 16 Issue: 2

Cite

APA Topal, K. (2024). New Sequence Spaces Derived From the Composition of Integrated and Differentiated Spaces and Binomial Matrix. Turkish Journal of Mathematics and Computer Science, 16(2), 373-385. https://doi.org/10.47000/tjmcs.1321967
AMA Topal K. New Sequence Spaces Derived From the Composition of Integrated and Differentiated Spaces and Binomial Matrix. TJMCS. December 2024;16(2):373-385. doi:10.47000/tjmcs.1321967
Chicago Topal, Kübra. “New Sequence Spaces Derived From the Composition of Integrated and Differentiated Spaces and Binomial Matrix”. Turkish Journal of Mathematics and Computer Science 16, no. 2 (December 2024): 373-85. https://doi.org/10.47000/tjmcs.1321967.
EndNote Topal K (December 1, 2024) New Sequence Spaces Derived From the Composition of Integrated and Differentiated Spaces and Binomial Matrix. Turkish Journal of Mathematics and Computer Science 16 2 373–385.
IEEE K. Topal, “New Sequence Spaces Derived From the Composition of Integrated and Differentiated Spaces and Binomial Matrix”, TJMCS, vol. 16, no. 2, pp. 373–385, 2024, doi: 10.47000/tjmcs.1321967.
ISNAD Topal, Kübra. “New Sequence Spaces Derived From the Composition of Integrated and Differentiated Spaces and Binomial Matrix”. Turkish Journal of Mathematics and Computer Science 16/2 (December 2024), 373-385. https://doi.org/10.47000/tjmcs.1321967.
JAMA Topal K. New Sequence Spaces Derived From the Composition of Integrated and Differentiated Spaces and Binomial Matrix. TJMCS. 2024;16:373–385.
MLA Topal, Kübra. “New Sequence Spaces Derived From the Composition of Integrated and Differentiated Spaces and Binomial Matrix”. Turkish Journal of Mathematics and Computer Science, vol. 16, no. 2, 2024, pp. 373-85, doi:10.47000/tjmcs.1321967.
Vancouver Topal K. New Sequence Spaces Derived From the Composition of Integrated and Differentiated Spaces and Binomial Matrix. TJMCS. 2024;16(2):373-85.