Research Article
Year 2025,
Volume: 46 Issue: 3, 590 - 594, 30.09.2025
Abstract
This study focuses on the higher-order difference operator Δ^m, which is defined via an (m+1)-band matrix and serves as a generalization of classical operators such as ∆, Δ^2, B(r,s) and B(r,s,t). Within the framework of the sequence space l_p for 1
References
- [1] Altay, B., Başar, F., On the fine spectrum of the difference operator on and , Inf. Sci., 168 (2004) 217–224.
- [2] Altay, B., Başar, F., The fine spectrum and the matrix domain of the difference operator on the sequence space , , Commun. Math. Anal., 2(2) (2007) 1–11.
- [3] Altay, B., Başar, F., On the fine spectrum of the generalized difference operator over the sequence spaces and , Int. J. Math. Math. Sci., 18 (2005) 3005–3013.
- [4] Akhmedov, A.M., Başar, F., On the fine spectra of the difference operator over the sequence space , Demonstr. Math., 39(3) (2006) 586–595.
- [5] Akhmedov, A.M., Başar, F., On the fine spectra of the difference operator over the sequence space, , Acta. Math. Sin. (Engl. Ser.), 23(10) (2007) 1757–1768.
- [6] Durna, N., Yıldırım, M., Kılıç, R., Partition of the spectra for the generalized difference operator on the sequence space , Cumhuriyet Sci. J., 39(1) (2018) 7–15.
- [7] Srivastava, P.D., Kumar, S., On the fine spectrum of the generalized difference operator over the sequence space, Commun. Math. Anal., 6(1) (2009) 8–21.
- [8] Srivastava, P.D., Kumar, S., Fine spectrum of the generalized difference operator on sequence space , Thai. J. Math., 8(2) (2010) 221–233.
- [9] Akhmedov, A.M., El-Shabrawy, S.R., On the fine spectrum of the operator over the sequence space, Comput. Math. Appl., 61 (2011) 2994–3002.
- [10] Dutta, S., Baliarsingh, P., On the fine spectra of the generalized difference operator on the sequence space, Appl. Math. Comput., 219 (2012) 1776–1784.
- [11] Dutta, S., Baliarsingh, P., On the spectrum of order generalized difference operator over the sequence space , Bol. Soc. Paran. Mat., 31(2) (2013) 235–244.
- [12] Durna, N., Yıldırım, M., Ünal, Ç., On the fine spectrum of generalized lower triangular double band matrices Over The Sequence Space, Cumhuriyet Sci. J., 37(3) (2016) 281–291.
- [13] Durna, N., Subdivision of spectra for some lower triangular doule-band matrices as operators on , Ukrain. Mat. Zh., 70(7) (2018) 913–922.
- [14] Durna, N., Kılıç, R., On the spectrum and fine spectrum of the upper triangular double band matrix over the sequence space , Honam Mathematical J., 45(4) (2023) 598-609.
- [15] Durna, N., Mursaleen, M. and Kılıç, R., Spectra and fine spectra of the generalized upper difference operator with triple repetition on the Hahn sequence space, Mathematica Slovaca, 72(3) (2022) 719-736.
- [16] Durna, N., Spectra and fine spectra of the upper triangular band matrix on the Hahn sequence space, Mathematical Communications, 25(1) (2020) 49-66.
- [17] Rani, J., Patra, A., Srivastava, P. D., Spectrum and Fine Spectrum of Band Matrices Generated by Oscillatory Sequences, Operators and Matrices, 18(4) (2024) 805-831.
- [18] Bilgiç, H., Furkan, H., On the fine spectrum of the generalized difference operator over the sequence spaces and , Nonlinear Anal., 68(3) (2008) 499-506.
- [19] Furkan, H., Bilgiç, H., Altay, B., On the fine spectrum of the operator over the sequence space and , Comput. Math. Appl., 60(7) (2010) 897–908.
- [20] Baliarsingh, P., Mursalen, M., Rakocevic, V., A survey on the spectra of the difference operators over the Banach space , RACSAM, 115(57) (2021) 1–17.
- [21] Taylor, R. B., Introduction to functional analysis Wiley, New York, (1980).
- [22] Wilansky, A., Summability Through Functional Analysis, North-Holland Mathematics Studies, Amsterdam, (1984).
- [23] Goldberg, S., Unbounded Linear Operators, McGraw Hill, New York (1966).
- [24] Tuğutlu M., Durna N., On the Spectrum of the difference operator over the sequence space , 1 st ICSAR, Konya, Turkey, 2022,362-366.
- [25] Appell, J., Pascale, E.D., Vignoli, A., Nonlinear Spectral Theory, Walter de Gruyter, Berlin New York, (2004).
There are 25 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Operator Algebras and Functional Analysis |
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | September 30, 2025 |
| Submission Date | July 26, 2025 |
| Acceptance Date | September 15, 2025 |
| Published in Issue | Year 2025 Volume: 46 Issue: 3 |
