آمار
| تعداد نشریات | 26 |
| تعداد شماره‌ها | 447 |
| تعداد مقالات | 4,557 |
| تعداد مشاهده مقاله | 5,380,005 |
| تعداد دریافت فایل اصل مقاله | 3,580,078 |
Generalized Cesaro tensor and it's properties | ||
| Journal of Mahani Mathematical Research | ||
| دوره 13، شماره 2 - شماره پیاپی 27، آبان 2024، صفحه 93-106 اصل مقاله (495.29 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2023.21701.1456 | ||
| نویسندگان | ||
| Javad Fathi* ؛ Fatemeh Saieedi؛ Mostafa Zangiabadi | ||
| Department of Mathematics, University of Hormozgan, P.O. BOX 3995, Bandar Abbas, Iran | ||
| چکیده | ||
| Recently, infinite and finite dimensional generalized Hilbert tensors have been introduced. In this paper, the authors further introduce infinite and finite dimensional generalized Cesaro tensors as a generalization of Cesaro matrices and discuss the properties of these structured tensors. Next, some upper bounds of $Z_{1}$-spectral radius of generalized Cesaro tensors and generalized Hilbert tensors are given, which improves the existing ones. Finally, we obtain conditions under which a generalized Cesaro tensor is column sufficient tensor. | ||
| کلیدواژه‌ها | ||
| Generalized Ces´aro tensor؛ Z1-eigenvalue؛ Column sufficient tensor | ||
| مراجع | ||
|
[1] Brown, A., Halmos, P.R., & Shields, A.L. (1965). Cesaro operators, Acta sci. Math. (Szeged), 26, 125{137.
[2] Chang, K.C., & Zhang, T. (2013). On the uniqueness and non-uniqueness of the positive Z-eigenvector for transition probability tensors, J. Math. Anal. Appl., 408 , 525{540. https://doi.org/10.1016/j.jmaa.2013.04.019.
[3] Chen, H., Li, G., & Qi, L. (2016). Further results on Cauchy tensors and Hankel tensors, Appl. Math. Comput., 275 50{62. https://doi.org/10.1016/j.amc.2015.11.051.
[4] Chen, H., Qi, L., & Song, Y. (2016). Column sucient tensors and tensor complementarity problems, Front. Math. China., 13 (2018), 255{276. https://doi.org/10.1007/s11464-018-0681-4.
[5] Duttaa, A., Deba, R., & Das, A. K. (2022). On some properties of !-uniqueness in tensor complementarity problem, https://arxiv.org/pdf/2203.08582.
[6] Frazer, H. (1946). Note on Hilbert's Inequality, J. London Math. Soc., 1, 7-9. https://doi.org/10.1112/jlms/s1-21.1.7.
[7] Ingham, A.E. (1936). A note on Hilbert's Inequality, J. London Math. Soc., 1, 237{240. https://doi.org/10.1016/S0096-3003(02)00107-8.
[8] Kriete, T.L., & Trutt, D. (1971). The Cesaro operator in l2 is subnormal, Amer. J. Math., 93, 215{225.
[9] Li, W., Liu, D., & Vong, S.W. (2015). Z-eigenpair bounds for an irreducible nonnegative tensor, Linear Algebra Appl., 483, 182{199. https://doi.org/10.1016/j.laa.2015.05.033.
[10] Li, W., & Ng, M.K. (2014). On the limiting probability distribution of a transition probability tensor, Linear and Multilinear Algebra, 62, 362{385. https://doi.org/10.1080/03081087.2013.777436.
[11] Lim, L. H., (2005). Singular values and eigenvalues of tensors: A variational approach, in: Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 05, vol. 1, IEEE Computer Society Press, Piscataway, NJ 129{132. https://doi.org/10.48550/arXiv.math/0607648.
[12] Mei, W., & Song, Y. (2017). In nite and nite dimensional generalized Hilbert tensors, Linear Algebra Appl., 532, 8{24. https://doi.org/10.1016/j.laa.2017.05.052.
[13] Meng, J., & Song, Y. (2020). Upper bounds for Z1-eigenvalues of generalized Hilbert tensors, J. Ind. Manag. Optim, 16, 911{918. https://doi.org/10.48550/arXiv.1712.04253
[14] Qi, L., & Luo, Z. (2017). Tensor Analysis: Spectral Theory and Special Tensors, Society for Industrial and Applied Mathematics. [15] Qi, L. (2015). Hankel tensors: Associated Hankel matrices and Vandermonde decomposition, Commun. Math. Sci., 13, 113{125. https://doi.org/10.48550/arXiv.1310.5470.
[16] Qi, L. (2005). Eigenvalues of a real supersymmetric tensor, J. Symbolic Comput, 40, 1302{1324. https://doi.org/10.1016/j.jsc.2005.05.007.
[17] Song, Y., & Qi, L. (2014). In nite and nite dimensional Hilbert tensors, Linear Algebra Appl., 451, 1{14. https://doi.org/10.48550/arXiv.1401.4966.
[18] Rhaly, H.C. (1984). Generalized Cesaro matrices, Cand. Math. Bull., 27, 417{422.
[19] Wei, Y., & Ding, W. (2016). Theory and computation of tensors: multi-dimensional arrays, Academic Press. | ||
|
آمار تعداد مشاهده مقاله: 132 تعداد دریافت فایل اصل مقاله: 210 |
||