TY - JOUR T1 - Subdivisions of the Spectra for Difference Operator Δ^m over the Sequence Space l_p AU - Kiliç, Rabia PY - 2025 DA - September Y2 - 2025 JF - Cumhuriyet Science Journal JO - CSJ PB - Sivas Cumhuriyet University WT - DergiPark SN - 2587-2680 SP - 590 EP - 594 VL - 46 IS - 3 LA - en AB - 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 KW - Spectrum KW - Fine spectrum KW - Generalized difference operator KW - Band matrix CR - [1]      Altay, B., Başar, F., On the fine spectrum of the difference operator on and , Inf. Sci., 168 (2004) 217–224. CR - [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. CR - [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. CR - [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. CR - [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. CR - [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. CR - [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. CR - [8]   Srivastava, P.D., Kumar, S., Fine spectrum of the generalized difference operator on sequence space , Thai. J. Math., 8(2) (2010) 221–233. CR - [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. CR - [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. CR - [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. CR - [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. CR - [13]    Durna, N., Subdivision of spectra for some lower triangular doule-band matrices as operators on , Ukrain. Mat. Zh., 70(7) (2018) 913–922. CR - [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. CR - [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. CR - [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. CR - [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. CR - [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. CR - [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. CR - [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. CR - [21]    Taylor, R. B., Introduction to functional analysis Wiley, New York, (1980). CR - [22]    Wilansky, A., Summability Through Functional Analysis, North-Holland Mathematics Studies, Amsterdam, (1984). CR - [23]    Goldberg, S., Unbounded Linear Operators, McGraw Hill, New York (1966). CR - [24]    Tuğutlu M., Durna N., On the Spectrum of the difference operator over the sequence space , 1 st ICSAR, Konya, Turkey, 2022,362-366. CR - [25]    Appell, J., Pascale, E.D., Vignoli, A., Nonlinear Spectral Theory, Walter de Gruyter, Berlin New York, (2004). UR - https://dergipark.org.tr/en/pub/csj/article/1751711 L1 - https://dergipark.org.tr/en/download/article-file/5094144 ER -