SavedAdd your journal

Journals / Istanbul Journal of Mathematics / 2026 / Volume: 4 Issue: 1

Some New Sequence Spaces Generated by Cesàro Matrix of Order 𝑚 and Related Results

Medine Yeşilkayagil(USAK UNIVERSITY)0000-0001-8447-9263
Feyzi Başar(INONU UNIVERSITY)0000-0002-9949-1481
Pages
—
Publication Date
2026-06-30
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we establish some identities or estimates for the operator norms and the Hausdorff measures of non-compactness of certain matrix operators on the spaces 𝐶𝑚𝑝 and 𝐶∞𝑚 for 1 ≤ 𝑝 < ∞.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We essentially examine the sequence spaces 𝐶𝑚𝑝 and 𝐶∞𝑚 generated by the domain of the Cesàro matrix 𝐶𝑚 of order 𝑚 in the spaces ℓ𝑝 and ℓ∞ of absolutely 𝑝-summable and bounded sequences, respectively.
📊
Key Findings & Data:We give some inclusion relation concerning to the spaces 𝐶𝑚𝑝 and 𝐶∞𝑚, and determine the 𝛼-, 𝛽- and 𝛾-duals of the spaces 𝐶1𝑚, 𝐶𝑚𝑝 and 𝐶∞𝑚.
💡
Conclusion & Impact:Finally, we establish some identities or estimates for the operator norms and the Hausdorff measures of non-compactness of certain matrix operators on the spaces 𝐶𝑚𝑝 and 𝐶∞𝑚 for 1 ≤ 𝑝 < ∞.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Sequence space · matrix domain · 𝛼-

Abstract

Let 0 < 𝑝 < ∞. We essentially examine the sequence spaces 𝐶𝑚𝑝 and 𝐶∞𝑚 generated by the domain of the Cesàro matrix 𝐶𝑚 of order 𝑚 in the spaces ℓ𝑝 and ℓ∞ of absolutely 𝑝-summable and bounded sequences, respectively. We give some inclusion relation concerning to the spaces 𝐶𝑚𝑝 and 𝐶∞𝑚, and determine the 𝛼-, 𝛽- and 𝛾-duals of the spaces 𝐶1𝑚, 𝐶𝑚𝑝 and 𝐶∞𝑚. After more, we characterize the classes of matrix transformations from the spaces 𝐶𝑚𝑝 and 𝐶∞𝑚 to any one of the classical spaces 𝑐0, 𝑐 and ℓ∞, where 0 < 𝑝 < ∞. We also give some knowledge about Steinhaus-type theorems and present this type theorem. Finally, we establish some identities or estimates for the operator norms and the Hausdorff measures of non-compactness of certain matrix operators on the spaces 𝐶𝑚𝑝 and 𝐶∞𝑚 for 1 ≤ 𝑝 < ∞.

🔖

Cite This Article

Yeşilkayagil, M., Başar, F. (2026). Some New Sequence Spaces Generated by Cesàro Matrix of Order 𝑚 and Related Results. Istanbul Journal of Mathematics, Volume: 4 Issue: 1. https://doi.org/10.26650/ijmath.2026.00032

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (21)

  1. Başar, F., 2022, Summability Theory and Its Applications, 2nd ed., CRC Press/Taylor & Francis Group, Boca Raton-London-New York. google scholar
  2. Boos, J., 2000., Classical and Modern Methods in Summability, Oxford University Press Inc., New York google scholar
  3. Cooke, R. G., 1950, Infinite Matrices and Sequence Spaces, Macmillan and Co. Limited, London. google scholar
  4. Goldenštein, L. S., Gohberg, I. T., Markus, A. S., 1957, Investigations of some properties of bounded linear operators with their 𝑞-norms, Učen. Zap. Kishinevsk. Univ., 29, 29-36. google scholar
  5. Grosse-Erdmann, K. G., 1993, Matrix transformations between the sequence spaces of Maddox, J. Math. Anal. Appl., 180, 223-238. google scholar
  6. Jarrah, A. M., Malkowsky, E., 2003, Ordinary, absolute and strong summability and matrix transformations, Filomat, 17, 59-78. google scholar
  7. Lascarides, C. G., Maddox, I. J., 1970, Matrix transformations between some classes of sequences, Proc. Camb. Phil. Soc., 68, 99-104. google scholar
  8. Maddox, I. J., 1967, On theorems of Steinhaus type, J. London Math. Soc., 42, 239-244. google scholar
  9. Malkowsky, E., Rakočević, V., 2000, An introduction into the theory of sequence spaces and measures of non-compactness, Zbornik radova, Mat. institut SANU (Beograd), 9(17), 143-234. google scholar
  10. Malkowsky, E., Rakočević, V., 2007, On matrix domains of triangles, Appl. Math. Comp., 187, 1146-1163. google scholar
  11. Malkowsky, E., Rakočević, V., 2020, Summability Methods and Applications, volume 24 of Posebna izdanja. Mathematical Institutus of the Serbian Academy of Sciences and Arts, Belgrade, Serbia. google scholar
  12. Mursaleen, M., Başar, F., 2020, Sequence Spaces: Topics in Modern Summability Theory, Series: Mathematics and Its Applications, CRC Press/Taylor, Francis Group, Boca Raton-London-New York. google scholar
  13. Mursaleen, M., Latif, A., 2012, Applications of measure of non-compactness in matrix operators on some sequence spaces, Abst. App. Anal., 2012, 1-20. google scholar
  14. Natarajan, P. N., 2021, Functional Analysis and Summability, CRC Press/Taylor & Francis Group, Boca Raton. google scholar
  15. Peyerimhoff, A., 1969, Lectures on Summability, volume 107 of Lecture Notes in Mathematics, Springer Verlag, Berlin-Heidelberg-New York. google scholar
  16. Roopaei, H., Foroutannia, D., İlkhan, M., Kara, E. E., 2020, Cesàro spaces and norm of operators on these matrix domains, Mediterr. J. Math., 17(4), 21. google scholar
  17. Stieglitz, M., Tietz, H., 1977, Matrix transformationen von folgenräumen eine ergebnisübersicht, Math. Z., 154(1), 1-16. google scholar
  18. Wilansky, A., 1984, Summability through Functional Analysis, North-Holland Mathematics Studies 85, Elsevier Science Publishers, Amesterdam-New York-Oxford. google scholar
  19. Yeşilkayagil Savaşcı, M., Başar, F., 2024, Some new Cesàro sequence spaces of order 𝛼, Ukrainian Math. J., 76(3), 484-500. google scholar
  20. Cooke, R. G., 1950, Infinite Matrices and Sequence Spaces, Macmillan and Co. Limited, London. google scholar
  21. Grosse-Erdmann, K. G., 1993, Matrix transformations between the sequence spaces of Maddox, J. Math. Anal. Appl., 180, 223-238. google scholar