Upper Bound of Difference Operator on Some Matrix Domains

Yıl 2021, Cilt: 4 Sayı: 1, 19 - 24, 30.04.2021

Lotfollah Karimi , Maryam Sinaei

https://doi.org/10.33187/jmsm.828002

Öz

In this study, we investigate the norm of difference operator on some sequence spaces such as Hilbert and Cesaro matrix domains. Therefore the present study is a complement for those results obtained in [1].

Anahtar Kelimeler

Difference operator, Hilbert matrix, Cesàro matrix, norm, sequence space

Kaynakça

• [1] H. Roopaei, D. Foroutannia, The norm of backward difference operator Dn on certain sequence spaces, Oper. Matrices, 12(3) (2018), 867-880.
• [2] H. Roopaei, Norm of Hilbert operator on sequence spaces, J. Inequal. Appl., 2020(117), (2020).
• [3] H. Kizmaz, On certain sequence spaces I, Canad. Math. Bull., 25(2) (1981), 169-176.
• [4] B. Altay, F. Basar, The fine spectrum and the matrix domain of the difference operator D on the sequence space `p, (0 < p < 1), Commun. Math. Anal., 2(2) (2007), 1–11.
• [5] F. Basar, B. Altay, On the space of sequences of p-bounded variation and related matrix mappings, Ukrainian Math. J., 55(1) (2003), 136–147.
• [6] C. P. Chen, D. C. Luor, Z. y. Ou, Extensions of Hardy inequality, J. Math. Anal. Appl., 273 (2002), 160–171.
• [7] B. Altay, F. Basar, Certain topological properties and duals of the matrix domain of a triangle matrix in a sequence space, J. Math. Anal. Appl., 336(1) (2007), 632–645.
• [8] E. E. Kara, M. Ilkhan, Some properties of generalized Fibonacci sequence spaces, Linear Multilinear Algebra, 64(11) (2016), 2208-2223.
• [9] F. Basar, Domain of the composition of some triangles in the space of p-summable sequences, AIP Conference Proceedings, 1611 (2014), 348–356.
• [10] H. Roopaei, F Basar, On the spaces of Cesaro absolutely p-summable, null, and convergent sequences, Math. Methods Appl. Sci., 44(5) (2021), 3670-3685.
• [11] H. Roopaei, T. Yaying, Quasi-Cesaro matrix and associated sequence spaces, Turk. J. Math., 45(1) (2021), 153-166.
• [12] H. Roopaei, M. ˙Ilkhan, Fractional Ces`aro matrix and its associated sequence space, Concr. Oper., 8(1), (2021), 24-39.
• [13] M. ˙Ilkhan, E. E. Kara, A new Banach space defined by Euler totient matrix operator, Oper. Matrices, 13(2) (2019), 527-544.
• [14] F. Bas¸ar, Summability Theory and Its Applications, Bentham Science Publishers, Istanbul, 2012.
• [15] H. Roopaei, D. Foroutannia, The norm of matrix operators on Ces`aro weighted sequence space, Linear Multilinear Algebra, 67(1) (2019), 175-185.
• [16] H. Roopaei, D. Foroutannia, The norms of certain matrix operators from `p spaces into `p(Dn) spaces, Linear Multilinear Algebra, 67(4) (2019), 767-776.
• [17] H. Roopaei, Norms of summability and Hausdorff mean matrices on difference sequence spaces, Math. Inequal. Appl., 22(3) (2019), 983-987.
• [18] H. Roopaei, A study on Copson operator and its associated sequence spaces, J. Inequal. Appl., 2020(120) (2020).
• [19] H. Roopaei, A study on Copson operator and its associated sequence spaces II, J. Inequal. Appl., 2020(239) (2020).
• [20] H. Roopaei, Bounds of operators on the Hilbert sequence space, Concr. Oper., 7 (2020), 155-165.
• [21] H. Roopaei, Binomial operator as a Hausdorff operator of the Euler type, Constr. Math. Anal., 3(4) (2020), 165-177.
• [22] G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities, 2nd edition, Cambridge University Press, Cambridge, 2001.
• [23] Ng P-N, Lee P-Y, Cesaro sequence spaces of non-absolute type, Comment. Math. Prace Mat., 20(2) (1978), 429-433.
• [24] M. Sengonul, F. Basar, Cesaro sequence spaces of non-absolute type which include the spaces c0 and c, Soochow J. Math., 31(1) (2005), 107-119.
• [25] H. Roopaei, D. Foroutannia, M. Ilkhan, E. E. Kara, Cesaro Spaces and Norm of Operators on These Matrix Domains, Mediterr. J. Math., 17, 121 (2020).
• [26] G. Bennett, Factorizing the classical inequalities, Mem. Amer. Math. Soc., 576 (1996).