New Integrated and Differentiated Sequence Spaces ∫ b_p^(r,s) and db_p^(r,s)

Year 2024, Volume: 28 Issue: 5, 1076 - 1086

Kübra Topal

Abstract

In this work, we construct new sequence spaces by combining the integrated and differentiated sequence spaces with the binomial matrix. Firstly, we provide information about basic matters such as sequence spaces and matrix domain. Subsequently we briefly summarize some sequence spaces generated by the binomial matrix. Thereafter, we define the integrated and differentiated sequence spaces and establish the new sequence spaces. Afterwards, we examine some properties and the inclusion relations of these new sequence spaces. We also determine the α, β and γ-duals of the integrated and differentiated sequence spaces. Finally, we characterize some matrix classes associated with the new sequence spaces.

Keywords

Matrix transformations, Matrix domain, α-β-and γ-duals, Matrix classes

References

• B. Choudhary, S. Nanda, Functional Analysis with Applications. New Delhi: Wiley, 1989.
• A. Wilansky, Summability Through Functional Analysis. Amsterdam: North-Holland mathematics studies, 1984.
• G. Goes, S. Goes, “Sequences of Bounded Variation and Sequences of Fourier Coefficients. I”, Mathematische Zeitschrift, 118, pp. 93–102, 1970.
• M. Kirişci, “Integrated and Differentiated Sequence Spaces”, Journal Nonlinear Analysis and Application, 1, pp. 2-16, 2015.
• M. Kirişci, “Reisz Type Integrated and Differentiated Sequence Spaces”, Bulletin of Mathematical Analysis and Applications, 7, 2, pp. 14-27, 2015.
• M. Kirişci, “Integrated and Differentiated Sequence Spaces and Weighted Mean”, Journal of Advances in Mathematics and Computer Science, 29, 1, pp. 1-11, 2018.
• M. C. Bisgin, “The Binomial Sequence Spaces of Nonabsolute Type”, Journal Of Inequalities and Applications, 309, 2016.
• M. C. Bisgin, “The Binomial Sequence Spaces Which Include the Spaces l_p and l_∞ and Geometric Properties”, Journal of Inequalities and Applications, 304, 2016.
• M. C. Bişgin, “A Note on the Sequence Space b_p^(r,s) (G)”, Cumhuriyet Science Journal, vol. 38, 4, pp. 11-25, 2017.
• A. Sönmez, “Some Notes on the New Sequence Space b_p^(r,s) (D)”, Gazi University Journal of Science, vol. 33, 2, pp. 476-490, 2020.
• M. Stieglitz, H. Tietz, “Matrixtransformationen von Folgenräumen Eine Ergebnisübersicht”, Mathematische Zeitschrift. vol, 154, pp. 1–16, 1977.