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

Medine Yeşilkayagil; Feyzi Başar

doi:10.26650/ijmath.2026.00032

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

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 < ∞.

Keywords

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Medine Yeşilkayagil
0000-0001-8447-9263
Türkiye

Feyzi Başar
0000-0002-9949-1481
Türkiye

Publication Date

June 30, 2026

Submission Date

October 27, 2025

Acceptance Date

May 15, 2026

Published in Issue

Year 2026 Volume: 4 Number: 1

DOI

https://doi.org/10.26650/ijmath.2026.00032

IZ

https://izlik.org/JA55BJ82FJ

Cite

RIS / Bibtex

APA

Yeşilkayagil, M., & Başar, F. (2026). Some New Sequence Spaces Generated by Cesàro Matrix of Order 𝑚 and Related Results. Istanbul Journal of Mathematics, 4(1), 8-22. https://doi.org/10.26650/ijmath.2026.00032

AMA

1.Yeşilkayagil M, Başar F. Some New Sequence Spaces Generated by Cesàro Matrix of Order 𝑚 and Related Results. Istanbul Journal of Mathematics. 2026;4(1):8-22. doi:10.26650/ijmath.2026.00032

Chicago

Yeşilkayagil, Medine, and Feyzi Başar. 2026. “Some New Sequence Spaces Generated by Cesàro Matrix of Order 𝑚 and Related Results”. Istanbul Journal of Mathematics 4 (1): 8-22. https://doi.org/10.26650/ijmath.2026.00032.

EndNote

Yeşilkayagil M, Başar F (June 1, 2026) Some New Sequence Spaces Generated by Cesàro Matrix of Order 𝑚 and Related Results. Istanbul Journal of Mathematics 4 1 8–22.

IEEE

[1]M. Yeşilkayagil and F. Başar, “Some New Sequence Spaces Generated by Cesàro Matrix of Order 𝑚 and Related Results”, Istanbul Journal of Mathematics, vol. 4, no. 1, pp. 8–22, June 2026, doi: 10.26650/ijmath.2026.00032.

ISNAD

Yeşilkayagil, Medine - Başar, Feyzi. “Some New Sequence Spaces Generated by Cesàro Matrix of Order 𝑚 and Related Results”. Istanbul Journal of Mathematics 4/1 (June 1, 2026): 8-22. https://doi.org/10.26650/ijmath.2026.00032.

JAMA

1.Yeşilkayagil M, Başar F. Some New Sequence Spaces Generated by Cesàro Matrix of Order 𝑚 and Related Results. Istanbul Journal of Mathematics. 2026;4:8–22.

MLA

Yeşilkayagil, Medine, and Feyzi Başar. “Some New Sequence Spaces Generated by Cesàro Matrix of Order 𝑚 and Related Results”. Istanbul Journal of Mathematics, vol. 4, no. 1, June 2026, pp. 8-22, doi:10.26650/ijmath.2026.00032.

Vancouver

1.Medine Yeşilkayagil, Feyzi Başar. Some New Sequence Spaces Generated by Cesàro Matrix of Order 𝑚 and Related Results. Istanbul Journal of Mathematics. 2026 Jun. 1;4(1):8-22. doi:10.26650/ijmath.2026.00032