On the Domain of Nörlund Matrix in the Space of Bounded Variation Sequences

Author :Orhan Tug^1
1Mathematics Education Department, Ishik University, Erbil, Iraq

Abstract:  In this paper, we introduce a new sequence space bv(N^t) as the domain of Nörlund matrix N^t 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(N^t) . Finally, we characterize some new matrix classes over the space bv(N^t)  into some classical sequence space and vice versa.

Keywords:  Bounded Variation, Nörlund Mean, Sequence Spaces, Matrix Domain, Matrix Transformation, 2010 Mathematics Subject Classification. 46A45, 40C05.

doi: 10.23918/eajse.v3i2p111

Download the PDF Document from here.

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.