[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2017.57.4.631

On Some Binomial Difference Sequence Spaces

Meng, Jian (Department of Mathematics, Tianjin University of Technology)
Song, Meimei (Department of Mathematics, Tianjin University of Technology)

Publication Information

Kyungpook Mathematical Journal / v.57, no.4, 2017 , pp. 631-640 More about this Journal

Abstract

The aim of this paper is to introduce the binomial sequence spaces $b_0^{r,s}(\nabla)$ , $b_c^{r,s}(\nabla)$ and $b_{\infty}^{r,s}(\nabla)$ by combining the binomial transformation and difference operator. We prove that these spaces are linearly isomorphic to the spaces $c_0$ , c and ${\ell}_{\infty}$ , respectively. Furthermore, we compute the Schauder bases and the ${\alpha}-$ , ${\beta}-$ and ${\gamma}-duals$ of these sequence spaces.

Keywords

sequence space; matrix transformations; Schauder basis; $${\alpha$ $}-$$ , ${\beta}-$ and ${\gamma}-duals$ ;

Citations & Related Records

Reference

1	H. Dutta, Characterization of certain matrix classes involving generalized difference summability spaces, Appl. Sci., 11(2009), 60-67.
2	E. E. Kara and M Basarir, On compact operators and some Euler $B^{(m)}$ -difference sequence spaces, J. Math. Anal. Appl., 379(2011), 499-511. DOI
3	V. Karakaya and H. Polat, Some new paranormed sequence spaces defined by Euler and difference operators, Acta Sci. Math., 76(2010), 87-100.
4	H. Kizmaz, On certain sequence spaces, Canad. Math. Bull., 24(1981), 169-176. DOI
5	G. Kothe and O. Toeplitz, Linear Raume mit unendlich vielen koordinaten und Ringe unenlicher Matrizen, J. Reine Angew. Math., 171(1934), 193-226.
6	H. Polat and F. Basar, Some Euler spaces of difference sequences of order m. Acta Math. Sci Ser. B, 27(2007), 254-266. DOI
7	B. S. Reddy, On some generalized difference sequence spaces, Int. J. Math. Anal., 4(2010), 1519-1525.
8	M. Stieglitz and H Tietz, Matrixtransformationen von Folgenraumen. Eine Ergebnisubersicht, Math. Z., 154(1977), 1-16. DOI
9	B. C. Tripathy and A. Esi, A new type of difference sequence spaces. Intern. J. Sci. Technol., 1(2006), 11-14.
10	B. Altay and F. Basar, Some Euler sequence spaces of nonabsolute type, Ukrainian Math. J., 57(2005), 1-17. DOI
11	B. Altay, F. Basar and M. Mursaleen, On the Euler sequence spaces which include the spaces $l_p$ and $l_{\infty}$ . I, Inform. Sci., 176(2006), 1450-1462. DOI
12	B. Altay and H. Polat, On some new Euler difference sequence spaces, Southeast Asian Bull. Math., 30(2006), 209-220.
13	F. Basar, Summability Theory and its applications, Bentham Science Publishers, 2012.
14	B. Choudhary and S. Nanda, Functional analysis with application, John Wiley & Sons, New York, 1989.
15	C. Bektas, M. Et and R. Colak, Generalized difference sequence spaces and their dual spaces, J. Math. Anal. Appl., 292(2004), 423-432. DOI
16	M. C. Bisgin, The binomial sequence spaces of nonabsolute type, J. Inequal. Appl., 309(2016), 16 pp.
17	M. C. Bisgin, The binomial sequence spaces which include the spaces ${\ell}_p$ and ${\ell}_{\infty}$ and geometric properties, J. Inequal. Appl., 304(2016), 15 pp.