JOURNAL BROWSE
Search
Advanced SearchSearch Tips
On the Fibonacci Almost Convergent Sequence Space and Fibonacci Core
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 55, Issue 2,  2015, pp.355-372
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2015.55.2.355
 Title & Authors
On the Fibonacci Almost Convergent Sequence Space and Fibonacci Core
DEMIRIZ, SERKAN; KARA, EMRAH EVREN; BASARIR, METIN;
  PDF(new window)
 Abstract
In the present paper, by using the Fibonacci difference matrix, we introduce the almost convergent sequence space . Also, we show that the spaces and are linearly isomorphic. Further, we determine the -dual of the space and characterize some matrix classses on this space. Finally, Fibonacci core of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core.
 Keywords
Sequence spaces;almost convergence;Fibonacci matrix;-dual;matrix transformations;core theorems;
 Language
English
 Cited by
 References
1.
S. Banach, Theorie des operations lineaires. Chelsea Publishing company., New York (1978).

2.
G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math., 80(1948), 167-190. crossref(new window)

3.
J. Boos, Classical and Modern Methods in Summability, Oxford University Press Inc, New York, 2000.

4.
M. Sengonul and K. Kayaduman, On the Riesz almost convergent sequence space, Abstr. Appl. Anal. Volume 2012, Article ID 691694, 18 pages, doi:10.1155/2012/691694. crossref(new window)

5.
K. Kayaduman and M. Sengonul, The spaces of Cesaro almost convergent sequences and core Theorems, Acta Math. Sci., 32B(6)(2012), 2265-2278.

6.
F. Basar and M. Kirisci, Almost convergence and generalized difference matrix, Comput. Math. Appl., 61(2011), 602-611. crossref(new window)

7.
A. Sonmez, Almost convergence and triple band matrix, Math. Comput. Model., 57(9-10)(2012), 2393-2402.

8.
E. E. Kara and K. Elmaagac, On the u-difference almost sequence space and matrix transformations, Inter. J. Modern Math. Sci., 8(1)(2013), 57-76.

9.
Mursaleen, Invariant means and some matrix transformations, Indian J. Pure Appl. Math., 25(3)(1994), 353-359.

10.
M. Mursaleen, E. Savas, M. Aiyub and S. A. Mohuiddine, Matrix transformations between the spaces of Cesaro sequences and invariant means, Int. J. Math. Math. Sci. Volume 2006 (2006), Article ID 74319, 8 pages, doi:10.1155/IJMMS/2006/74319. crossref(new window)

11.
J.P. Duran, Infinite matrices and almost convergence, Math. Z., 128(1972), 75-83. crossref(new window)

12.
F. Basar and I. Solak, Almost-coercive matrix transformations, Rend. Mat. Appl., (7)11(2)(1991), 249-256.

13.
F. Basar and R. Colak, Almost-conservative matrix transformations, Turkish J. Math., 13(3)(1989), 91-100.

14.
F. Basar, f-conservative matrix sequences, Tamkang J. Math., 22(2)(1991), 205-212.

15.
J. P. King, Almost summable sequences, Proc. Amer. Math. Soc., 17(1966), 1219-1225. crossref(new window)

16.
J. A. Siddiqi, Infinite matrices summing every almost periodic sequences, Pacific. J. Math., 39(1)(1971), 235-251. crossref(new window)

17.
Qamaruddin and S. A. Mohuiddine, Almost convergence and some matrix transformations, Filomat, 21(2)(2007), 261-266. crossref(new window)

18.
S. Nanda, Matrix transformations and almost boundedness, Glasnik Mat., 34(14)(1979), 99-107.

19.
S. A. Gupkari, Some new sequence spaces and almost convergence, Filomat, 22(2)(2008), 59-64. crossref(new window)

20.
Mursaleen, Invariant means and some matrix transformations, Indian J. Pure Appl. Math., 25(3)(1994), 353-359.

21.
G. Das, B. Kuttner and S. Nanda, On absolute almost convergence, J. Math. Anal. Appl., 161(1)(1991), 50-56. crossref(new window)

22.
R. G. Cooke, Infinite Matrices and Sequence Spaces, Mcmillan, New York, 1950.

23.
A. A. Shcherbakov, Kernels of sequences of complex numbers and their regular transformations, Math. Notes, 22(1977), 948-953. crossref(new window)

24.
H. Steinhaus, Quality control by sampling, Collog. Math., 2(1951), 98-108.

25.
J. A. Fridy and C. Orhan, Statistical core theorems, J. Math. Anal. Appl., 208(1997), 520-527. crossref(new window)

26.
H. S. Allen, T-transformations which leave the core of every bounded sequence invariant, J. London Math. Soc., 19(1944), 42-46. crossref(new window)

27.
J. Connor, J. A. Fridy and C. Orhan, Core equality results for sequences, J. Math. Anal. Appl., 321(2006), 515-523. crossref(new window)

28.
C. Cakan and H. Coskun, Some new inequalities related to the invariant means and uniformly bounded function sequences, Appl. Math. Lett., 20(6)(2007), 605-609. crossref(new window)

29.
H. Coskun and C. Cakan, A class of statistical and ${\sigma}$-conservative matrices, Czechoslovak Math. J., 55(3)(2005), 791-801.

30.
H. Coskun, C. Cakan and M. Mursaleen, On the statistical and ${\sigma}$-cores, Studia Math., 154(1)(2003), 29-35. crossref(new window)

31.
T. Koshy, Fibonacci and Lucas Numbers with Applications. Wiley, 2001.

32.
E. E. Kara, Some topological and geometrical properties of new Banach sequence spaces, J. Inequal. Appl., 2013(38)(2013), 15 pages. crossref(new window)

33.
E. E. Kara, M. Basarir and M. Mursaleen, Compact operators on the Fibonacci difference sequence spaces ${\ell}_p({\hat{F}})$ and ${\ell}_{\infty}({\hat{F}})$, 1st International Eurasian Conference on Mathematical Sciences and Applications, Prishtine-Kosovo, September 3-7, 2012.

34.
M. Basarir, F. Basar and E. E. Kara, On The Spaces of Fibonacci Difference Null and Convergent Sequences, arXiv:1309.0150.

35.
E. E. Kara and S. Demiriz, Some new paranormed Fibonacci difference sequence spaces, 2st International Eurasian Conference on Mathematical Sciences and Applications, Sarajevo-Bosnia and Herzegouina, August 26-29, 2013.

36.
F. Basar, Summability Theory and Its Applications, Bentham Science Publishers, e-books, Monographs, Istanbul, 2012.

37.
A. M. Jarrah and E. Malkowsky, BK spaces, bases and linear operators, Ren. Circ. Mat. Palermo, II 52(1990), 177-191.

38.
S. Simons, Banach limits, infinite matrices and sublinear functionals, J. Math. Anal. Appl., 26(1969), 640-655. crossref(new window)

39.
K. Demirci, A-statistical core of a sequence, Demonstratio Math., 33(2000), 43-51.