On new difference sequence spaces via Cesà ro mean
DOI:
https://doi.org/10.5269/bspm.52561Abstract
In the present article, we define certain a set of new classes of sequence spaces by using Ces\`{a}ro mean and difference operator $\Delta^r\;\;r\in\mathbb{N}_0=\{0,1,2,3,\dots\}$. Also, we study the topological structures of the defined classes and determine their $\alpha-,\beta-$ and $\gamma-$ duals. Matrix transformations of given classes with their basic sequence spaces are characterized.
References
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[2] B. Altay, F. Bassar, Some paranormed sequence spaces of non absolute type derived by weighted mean, J. Math. Anal. Appl. 319(2) (2006) 494-508.
[3] C. Asma, R. Colak, On the Kothe-Toeplitz duals of some generalized sets of difference sequences, Demonstratio Math. 33 (2000) 797-803.
[4] P. Baliarsingh, Some new difference sequence spaces of fractional order and their dual spaces, Appl. Math. Comput. 219(18) (2013) 9737-9742.
[5] P. Baliarsingh, On a fractional difference operator, Alexandria Eng. J. 55(2) (2016) 1811-1816.
[6] M. Basarir, On the generalized Riesz B-difference sequence spaces, Filomat, 24(4)(2010) 35-52.
[7] M. Et, R. Colak, On some generalized difference sequence spaces, Soochow J. Math. 21 (1995) 377-386.
[8] K. G. Grosse-Erdmann, Matrix transformations between the sequence spaces of Maddox, Second edition, J. Math. Anal. Appl., 180 (1993)223-238.
[9] H. Kizmaz, On certain sequence spaces, Canad. Math. Bull., 24(2) (1981) 169-176.
[10] I. J. Maddox, Paranormed sequence spaces generated by in nite matrices, Proc. Cambridge Philos. Soc., 64 (1968) 335-340.
[11] I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. Oxford, 18(2) (1967) 345-355.
[12] E. Malkowsky, M. Mursaleen, S. Suantai, The dual spaces of sets of difference sequences of order m and martix transformations, Acta Math. Sin. (English Series), 23(3) (2007) 521-532.
[13] H.K. Mishra, S. Nanda., P. Baliarsingh, On new sequence spaces using modulus function, Panamerican Math. J. 27(1) (2017) 52-66
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2022-12-23
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