On the Domain of Nörlund Matrix in the Space of Bounded Variation Sequences
DOI:
https://doi.org/10.23918/eajse.v3i2p111Keywords:
Bounded Variation, Nörlund Mean, Sequence Spaces, Matrix Domain, Matrix Transformation, 2010 Mathematics Subject Classification, 46A45, 40C05Abstract
In this paper, we introduce a new sequence space bv(Nt) as the domain of Nörlund matrix Nt in the space of all sequences of bounded variation. Firstly, we give some topological properties and inclusion relations. Moreover, we determine the α-, β- and γ- duals of the space bv(Nt) . Finally, we characterize some new matrix classes over the space bv(Nt) into some classical sequence space and vice versa.
References
Al-Jarrah, A. M., & Malkowsky, E. (1998). BK spaces, bases and linear operators. Rend. Circ. Mat.
Palermo (2) Suppl, 52, 177-191.
Duran, J. P. (1972). Infinite matrices and almost-convergence. Mathematische Zeitschrift, 128(1),
75-83.
King, J. P. (1966). Almost summable sequences. Proceedings of the American Mathematical
Society, 17(6), 1219-1225.
Kirişci, M. (2014). The sequence space bv and some applications. arXiv preprint arXiv:1403.1720.
Mears, F. M. (1943). The inverse Nörlund mean. Annals of Mathematics, 401-410.
Ng, P. N. (1978). Matrix Transformations on Cesaro Sequence Spaces of a Nonabsolute Type. Lee
Kong Chian Institute of Mathematics & Computer Science, Nanyang University.
Şengönül, M., & Başar, F. (2005). Some new cesaro sequence spaces of non-absolute type which
include. Soochow Journal of Mathematics, 31(1), 107-119.
Sıddıqi, J. A. (1971). Infinite matrices summing every almost periodic sequences. Pac. J.
Math, 39(1), 235-251.
Sönmez, A. (2013). Almost convergence and triple band matrix. Mathematical and Computer
Modelling, 57(9), 2393-2402.
Stieglitz, M., & Tietz, H. (1977). Matrix transformationen von folgenräumen eine
ergebnisübersicht. Mathematische Zeitschrift, 154(1), 1-16.
Tuǧ, O., & Başar, F. (2016). On the Spaces of Nörlund Almost Null and Nörlund Almost
Convergent Sequences. Filomat, 30(3), 773-783.
Tug, O., & Basar F. (2016). On the domain of Norlund mean in the spaces of null and convergent
sequences. TWMS J. Pure Appl. Math, 7.1 76-87.
Wang, C. S. (1978). On Nörlund sequence spaces. Tamkang J. Math, 9(1), 269-274.
Yeşilkayagil, M., & Başar, F. (2015). Spaces of Aλ-almost null and Aλ-almost convergent
sequences. Journal of the Egyptian Mathematical Society, 23(1), 119-126.
Yeşilkayagil, M., & Başar, F. ( 2014). On the Paranormed Nörlund Sequence Space of Nonabsolute
Type, Abst. Appl. Anal., vol. 2014, Article ID 858704, 9 pages, doi:10.1155/2014/858704
Yeşilkayagil, M., & Başar, F. (2017). Domain of the Nörlund Matrix in Some of Maddox’s
Spaces. Proc. Nat. Sci. India Sect. A 87(3), 363-371.
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