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http://dx.doi.org/10.5666/KMJ.2015.55.2.355

On the Fibonacci Almost Convergent Sequence Space and Fibonacci Core  

DEMIRIZ, SERKAN (Department of Mathematics, Gaziosmanpasa University)
KARA, EMRAH EVREN (Department of Mathematics, Duzce University)
BASARIR, METIN (Department of Mathematics, Sakarya University)
Publication Information
Kyungpook Mathematical Journal / v.55, no.2, 2015 , pp. 355-372 More about this Journal
Abstract
In the present paper, by using the Fibonacci difference matrix, we introduce the almost convergent sequence space $\hat{c}^f$. Also, we show that the spaces $\hat{c}^f$and $\hat{c}$ are linearly isomorphic. Further, we determine the ${\beta}$-dual of the space $\hat{c}^f$ 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; ${\beta}$-dual; matrix transformations; core theorems;
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  • Reference
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.   DOI
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.   DOI
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.   DOI   ScienceOn
7 A. Sonmez, Almost convergence and triple band matrix, Math. Comput. Model., 57(9-10)(2012), 2393-2402.   DOI
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.   DOI   ScienceOn
11 J.P. Duran, Infinite matrices and almost convergence, Math. Z., 128(1972), 75-83.   DOI
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.   DOI   ScienceOn
16 J. A. Siddiqi, Infinite matrices summing every almost periodic sequences, Pacific. J. Math., 39(1)(1971), 235-251.   DOI
17 Qamaruddin and S. A. Mohuiddine, Almost convergence and some matrix transformations, Filomat, 21(2)(2007), 261-266.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI   ScienceOn
26 H. S. Allen, T-transformations which leave the core of every bounded sequence invariant, J. London Math. Soc., 19(1944), 42-46.   DOI
27 J. Connor, J. A. Fridy and C. Orhan, Core equality results for sequences, J. Math. Anal. Appl., 321(2006), 515-523.   DOI   ScienceOn
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.   DOI   ScienceOn
29 H. Coskun and C. Cakan, A class of statistical and ${\sigma}$-conservative matrices, Czechoslovak Math. J., 55(3)(2005), 791-801.   DOI
30 H. Coskun, C. Cakan and M. Mursaleen, On the statistical and ${\sigma}$-cores, Studia Math., 154(1)(2003), 29-35.   DOI
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.   DOI
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.   DOI
39 K. Demirci, A-statistical core of a sequence, Demonstratio Math., 33(2000), 43-51.