On new difference sequence spaces via Cesàro mean

Pinakadhar Baliarsingh; Sudarsan Nanda

doi:10.5269/bspm.52561

Pinakadhar Baliarsingh Kalinga Institute of Industrial Technology deemed to be University https://orcid.org/0000-0002-5618-0413
Sudarsan Nanda Kalinga Institute of Industrial Technology deemed to be University https://orcid.org/0000-0001-8155-5363

Resumen

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.

Descargas

La descarga de datos todavía no está disponible.

Citas

Z. U. Ahmad, M. Mursaleen, Kothe-Toeplitz duals of some new sequence spaces and their martix maps, Publ. Inst. Math. (Beograd), 42(56) (1987) 57-61.

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. DOI: https://doi.org/10.1016/j.jmaa.2005.06.055

C. Asma, R. Colak, On the Kothe-Toeplitz duals of some generalized sets of difference sequences, Demonstratio Math. 33 (2000) 797-803. DOI: https://doi.org/10.1515/dema-2000-0412

P. Baliarsingh, Some new difference sequence spaces of fractional order and their dual spaces, Appl. Math. Comput. 219(18) (2013) 9737-9742. DOI: https://doi.org/10.1016/j.amc.2013.03.073

P. Baliarsingh, On a fractional difference operator, Alexandria Eng. J. 55(2) (2016) 1811-1816. DOI: https://doi.org/10.1016/j.aej.2016.03.037

M. Basarir, On the generalized Riesz B-difference sequence spaces, Filomat, 24(4)(2010) 35-52. DOI: https://doi.org/10.2298/FIL1004035B

M. Et, R. Colak, On some generalized difference sequence spaces, Soochow J. Math. 21 (1995) 377-386.

K. G. Grosse-Erdmann, Matrix transformations between the sequence spaces of Maddox, Second edition, J. Math. Anal. Appl., 180 (1993)223-238. DOI: https://doi.org/10.1006/jmaa.1993.1398

H. Kizmaz, On certain sequence spaces, Canad. Math. Bull., 24(2) (1981) 169-176. DOI: https://doi.org/10.4153/CMB-1981-027-5

I. J. Maddox, Paranormed sequence spaces generated by in nite matrices, Proc. Cambridge Philos. Soc., 64 (1968) 335-340. DOI: https://doi.org/10.1017/S0305004100042894

I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. Oxford, 18(2) (1967) 345-355. DOI: https://doi.org/10.1093/qmath/18.1.345

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. DOI: https://doi.org/10.1007/s10114-005-0719-x

H.K. Mishra, S. Nanda., P. Baliarsingh, On new sequence spaces using modulus function, Panamerican Math. J. 27(1) (2017) 52-66