Konferans Bildirisi
BibTex RIS Kaynak Göster

Some Algebraic and Topological Properties of New Lucas Difference Sequence Spaces

Yıl 2018, Cilt: 10, 144 - 152, 29.12.2018

Öz

Karakaş and Karabudak [14], introduced the Lucas sequence spaces $X(E)$  and studied their some properties. The main purpose of this study is to introduce the Lucas difference sequence spaces $c_0(\hat{L},\Delta)$ and $c(\hat{L},\Delta)$  by using the Lucas sequence sequences. Also, the spaces $c_0(\hat{L},\Delta)$ and $c(\hat{L},\Delta)$, are linearly isomorphic to spaces $c_0$ and $c$, respectively, have been proved. Besides this, the $\alpha-,\beta-$ and $\gamma-$duals of this spaces have been computed, their bases have been constructed and some topological properties of these spaces have been studied. Finally, the classes of matrices $(c_0(\hat{L},\Delta) : \mu)$ and $(c(\hat{L},\Delta) : \mu)$ have been characterized, where $\mu$ is one of
the sequence spaces $\ell_\infty, c$ and $c_0$ and derives the other characterizations for the special cases of $\mu$.

Kaynakça

  • Ahmad, Z.U., Mursaleen, M., \textit{K\"{o}the-Toeplitz duals of some new sequence spaces and their matrix maps. Publ. Inst.}, Math. (Belgr.) \textbf{42}(1987), 57-61.
  • Altay, B., Ba\c{s}ar, F., \textit{The fine spectrum and the matrix domain of the difference operator $\Delta$ on the sequence space $\ell_p, (0 < p < 1)$}, Commun.Math. Anal., \textbf{2}(2007), 1-11.
  • Altay, B., Ba\c{s}ar, F., \textit{Certain topological properties and duals of the domain of a triangle matrix in a sequence space}, J. Math. Anal. Appl., \textbf{336}(2007), 632-645.
  • Ba\c{s}ar, F., Domain of the composition of some triangles in the space of $p-$summable sequences for $0 < p \leq 1$, AIP Conference Proceedings, \textbf{1759}(2016), 020003-1-020003-6; doi: $10.1063/1.4959617.$
  • Ba\c{s}ar, F., Braha, N.L., {\em Euler-Ces\'{a}ro difference spaces of bounded, convergent and null sequences}, Tamkang J. Math. \textbf{47(4)}(2016), 405-420.
  • Ba\c{s}ar, F., \c{C}akmak, A.F., {\em Domain of triple band matrix $B(r, s, t)$ on some Maddox's spaces}, Ann. Funct. Anal., \textbf{3(1)}(2012), 32-48.
  • Ba\c{s}ar, F., Kiri\c{s}\c{c}i, M., {\em Almost convergence and generalized difference matrix}, Comput. Math. Appl., \textbf{61(3)}(2011), 602-611.
  • Ba\c{s}ar, F., Malkowsky, E., Altay, B., {\em Matrix transformations on the matrix domains of triangles in the spaces of strongly $C_1-$summable and bounded sequences}, Publ. Math. Debrecen, \textbf{73(1-2)}(2008), 193-213.
  • Ye\c{s}ilkayagil, M., Ba\c{s}ar, F., {\em Spaces of $A_\lambda-$almost null and $A_\lambda-$almost convergent sequences}, J. Egypt. Math. Soc., \textbf{23(2)}(2015), 119-126.
  • Ye\c{s}ilkayagil, M., Ba\c{s}ar, F., {\em On the paranormed N\"{o}rlund sequence space of non-absolute type}, Abstr. Appl. Anal., (2014), Article ID 858704, 9 pages, 2014. doi:$10.1155/2014/858704$.
  • Ba\c{s}ar, F., Summability Theory and Its Applications, Bentham Science Publishers, e-books, Monographs, Istanbul, 2012.
  • Ba\c{s}ar, F., Altay, B., \textit{On the space of sequences of $p-$bounded variation and related matrix mappings,} Ukrainian Math. J., \textbf{55}(2003), 136-147.
  • Ba\c{s}ar, F., Altay, B., Mursaleen, M., \textit{Some generalizations of the space $bv_p$ of $p-$bounded variation sequences}, Nonlinear Anal. TMA, \textbf{68}(2008), 273-287. \c{C}apan, H., Ba\c{s}ar, F., \textit{Domain of the double band matrix defined by Fibonacci numbers in the Maddox's space $\ell(p)$}, Electron. J. Math. Anal. Appl., \textbf{3(2)}(2015), 31-45.
  • \c{C}olak, R., Et, M., Malkowsky, E., \textit{Some Topics of Sequence Spaces}, in: Lecture Notes in Mathematics, F{\i}rat Univ. Press, (2004), 1-63, ISBN: 975-394-0386-6.
  • Das, A., Hazarika, B., \textit{Some properties of generalized Fibonacci difference bounded and $p-$absolutely convergent sequences}, Bol. Soc. Paran. Mat., \textbf{36(3)}(2018), 37-50.
  • Das, A., Hazarika, B., {\em Matrix transformation of Fibonacci band matrix on generalized bv-space and its dual spaces}, Bol. Soc. Paran. Mat., \textbf{36(3)}(2018), 41-52.
  • Kara, E.E., Ilkhan, M., \textit{Some properties of generalized Fibonacci sequence spaces,} Linear Multilinear Algebra, \textbf{64(11)}(2016), 2208-2223.
  • Ba\c{s}ar{\i}r, M., Ba\c{s}ar, F., Kara, E.E., \textit{On the spaces of Fibonacci difference absolutely $p-$summable, null and convergent sequences}, Sarajevo J. Math., \textbf{12(25)}(2016), 167-182.
  • Kara, E.E., Ba\c{s}ar{\i}r, M., Mursaleen, M., \textit{Compactness of matrix operators on some sequence spaces derived by Fibonacci numbers,} Kragujevac J. Math., \textbf{39(2)}(2015), 217-230.
  • Kara, E.E., Demiriz, S., \textit{Some new paranormed difference sequence spaces derived by Fibonacci numbers}, Miskolc Math. Notes., \textbf{16(2)}(2015), 907-923.
  • Karaka\c{s}, M., Karabudak, H., \textit{Lucas Sayilari ve Sonsuz Toeplitz Matrisleri \"{U}zerine Bir Uygulama}, Cumhuriyet Science Journal, \textbf{38(3)}(2017), 557-562.
  • K{\i}zmaz, H., \textit{On certain sequence spaces}, Canad.Math. Bull., \textbf{24}(1981), 169-176.
  • Kiri\c{s}\c{c}i, M., Ba\c{s}ar, F., \textit{Some new sequence spaces derived by the domain of generalized difference matrix,} Comput.Math. Appl., \textbf{60}(2010), 1299-1309.
  • Koshy, T., Fibonacci and Lucas Numbers with applications, Wiley, 2001.
  • Maddox, I.J., \textit{Continuous and K\"{o}the-Toeplitz duals of certain sequence spaces}, Proc. Camb. Philos. Soc., \textbf{65}(1965), 431-435.
  • Malkowsky, E., {\em Klassen von Matrixabbildungen in paranormierten FK-R\"{a}umen}, Analysis (Munich), \textbf{7}(1987), 275-292.
  • Malkowsky, E., \textit{Absolute and ordinary K\"{o}the-Toeplitz duals of some sets of sequences and matrix transformations}, Publ. Inst. Math. (Belgr.), 46(60)(1989), 97-103.
  • Mursaleen, M., \textit{Generalized spaces of difference sequences,} J. Math. Anal. Appl., \textbf{203(3)}(1996), 738-745.
  • Simons, S, \textit{The sequence spaces $\ell(p_v)$ and $m(p_v )$}, Proc. Lond. Math. Soc., \textbf{3(15)}(1965), 422-436.
  • S\"{o}nmez, A., \textit{Some new sequence spaces derived by the domain of the triple bandmatrix}, Comput.Math. Appl., \textbf{62}(2011), 641-650.
  • Stieglitz, M., Tietz, H., \textit{Matrix transformationen von folgenraumen eine ergebnisubersict,} Math. Z., \textbf{154}(1977), 1-16.
  • Tripathy, B.C., {\em Matrix transformation between some classes of sequences}, J. Math. Anal. Appl., \textbf{2}(1997), 448-450.
  • Tu\u{g}, O., Ba\c{s}ar, F., {\em On the domain of N\"{o}rlund mean in the spaces of null and convergent sequences}, TWMS J. Pure Appl. Math., \textbf{7(1)}(2016), 76-87.
  • Tu\u{g}, O., Ba\c{s}ar, F., {\em On the spaces of N\"{o}rlund almost null and N\"{o}rlund almost convergent sequences}, Filomat, \textbf{30(3)}(2016), 773-783.
  • Wilansky, A., Summability through Functional Analysis, North-HollandMathematics Studies 85, Amsterdam-Newyork-Oxford, 1984.
Yıl 2018, Cilt: 10, 144 - 152, 29.12.2018

Öz

Kaynakça

  • Ahmad, Z.U., Mursaleen, M., \textit{K\"{o}the-Toeplitz duals of some new sequence spaces and their matrix maps. Publ. Inst.}, Math. (Belgr.) \textbf{42}(1987), 57-61.
  • Altay, B., Ba\c{s}ar, F., \textit{The fine spectrum and the matrix domain of the difference operator $\Delta$ on the sequence space $\ell_p, (0 < p < 1)$}, Commun.Math. Anal., \textbf{2}(2007), 1-11.
  • Altay, B., Ba\c{s}ar, F., \textit{Certain topological properties and duals of the domain of a triangle matrix in a sequence space}, J. Math. Anal. Appl., \textbf{336}(2007), 632-645.
  • Ba\c{s}ar, F., Domain of the composition of some triangles in the space of $p-$summable sequences for $0 < p \leq 1$, AIP Conference Proceedings, \textbf{1759}(2016), 020003-1-020003-6; doi: $10.1063/1.4959617.$
  • Ba\c{s}ar, F., Braha, N.L., {\em Euler-Ces\'{a}ro difference spaces of bounded, convergent and null sequences}, Tamkang J. Math. \textbf{47(4)}(2016), 405-420.
  • Ba\c{s}ar, F., \c{C}akmak, A.F., {\em Domain of triple band matrix $B(r, s, t)$ on some Maddox's spaces}, Ann. Funct. Anal., \textbf{3(1)}(2012), 32-48.
  • Ba\c{s}ar, F., Kiri\c{s}\c{c}i, M., {\em Almost convergence and generalized difference matrix}, Comput. Math. Appl., \textbf{61(3)}(2011), 602-611.
  • Ba\c{s}ar, F., Malkowsky, E., Altay, B., {\em Matrix transformations on the matrix domains of triangles in the spaces of strongly $C_1-$summable and bounded sequences}, Publ. Math. Debrecen, \textbf{73(1-2)}(2008), 193-213.
  • Ye\c{s}ilkayagil, M., Ba\c{s}ar, F., {\em Spaces of $A_\lambda-$almost null and $A_\lambda-$almost convergent sequences}, J. Egypt. Math. Soc., \textbf{23(2)}(2015), 119-126.
  • Ye\c{s}ilkayagil, M., Ba\c{s}ar, F., {\em On the paranormed N\"{o}rlund sequence space of non-absolute type}, Abstr. Appl. Anal., (2014), Article ID 858704, 9 pages, 2014. doi:$10.1155/2014/858704$.
  • Ba\c{s}ar, F., Summability Theory and Its Applications, Bentham Science Publishers, e-books, Monographs, Istanbul, 2012.
  • Ba\c{s}ar, F., Altay, B., \textit{On the space of sequences of $p-$bounded variation and related matrix mappings,} Ukrainian Math. J., \textbf{55}(2003), 136-147.
  • Ba\c{s}ar, F., Altay, B., Mursaleen, M., \textit{Some generalizations of the space $bv_p$ of $p-$bounded variation sequences}, Nonlinear Anal. TMA, \textbf{68}(2008), 273-287. \c{C}apan, H., Ba\c{s}ar, F., \textit{Domain of the double band matrix defined by Fibonacci numbers in the Maddox's space $\ell(p)$}, Electron. J. Math. Anal. Appl., \textbf{3(2)}(2015), 31-45.
  • \c{C}olak, R., Et, M., Malkowsky, E., \textit{Some Topics of Sequence Spaces}, in: Lecture Notes in Mathematics, F{\i}rat Univ. Press, (2004), 1-63, ISBN: 975-394-0386-6.
  • Das, A., Hazarika, B., \textit{Some properties of generalized Fibonacci difference bounded and $p-$absolutely convergent sequences}, Bol. Soc. Paran. Mat., \textbf{36(3)}(2018), 37-50.
  • Das, A., Hazarika, B., {\em Matrix transformation of Fibonacci band matrix on generalized bv-space and its dual spaces}, Bol. Soc. Paran. Mat., \textbf{36(3)}(2018), 41-52.
  • Kara, E.E., Ilkhan, M., \textit{Some properties of generalized Fibonacci sequence spaces,} Linear Multilinear Algebra, \textbf{64(11)}(2016), 2208-2223.
  • Ba\c{s}ar{\i}r, M., Ba\c{s}ar, F., Kara, E.E., \textit{On the spaces of Fibonacci difference absolutely $p-$summable, null and convergent sequences}, Sarajevo J. Math., \textbf{12(25)}(2016), 167-182.
  • Kara, E.E., Ba\c{s}ar{\i}r, M., Mursaleen, M., \textit{Compactness of matrix operators on some sequence spaces derived by Fibonacci numbers,} Kragujevac J. Math., \textbf{39(2)}(2015), 217-230.
  • Kara, E.E., Demiriz, S., \textit{Some new paranormed difference sequence spaces derived by Fibonacci numbers}, Miskolc Math. Notes., \textbf{16(2)}(2015), 907-923.
  • Karaka\c{s}, M., Karabudak, H., \textit{Lucas Sayilari ve Sonsuz Toeplitz Matrisleri \"{U}zerine Bir Uygulama}, Cumhuriyet Science Journal, \textbf{38(3)}(2017), 557-562.
  • K{\i}zmaz, H., \textit{On certain sequence spaces}, Canad.Math. Bull., \textbf{24}(1981), 169-176.
  • Kiri\c{s}\c{c}i, M., Ba\c{s}ar, F., \textit{Some new sequence spaces derived by the domain of generalized difference matrix,} Comput.Math. Appl., \textbf{60}(2010), 1299-1309.
  • Koshy, T., Fibonacci and Lucas Numbers with applications, Wiley, 2001.
  • Maddox, I.J., \textit{Continuous and K\"{o}the-Toeplitz duals of certain sequence spaces}, Proc. Camb. Philos. Soc., \textbf{65}(1965), 431-435.
  • Malkowsky, E., {\em Klassen von Matrixabbildungen in paranormierten FK-R\"{a}umen}, Analysis (Munich), \textbf{7}(1987), 275-292.
  • Malkowsky, E., \textit{Absolute and ordinary K\"{o}the-Toeplitz duals of some sets of sequences and matrix transformations}, Publ. Inst. Math. (Belgr.), 46(60)(1989), 97-103.
  • Mursaleen, M., \textit{Generalized spaces of difference sequences,} J. Math. Anal. Appl., \textbf{203(3)}(1996), 738-745.
  • Simons, S, \textit{The sequence spaces $\ell(p_v)$ and $m(p_v )$}, Proc. Lond. Math. Soc., \textbf{3(15)}(1965), 422-436.
  • S\"{o}nmez, A., \textit{Some new sequence spaces derived by the domain of the triple bandmatrix}, Comput.Math. Appl., \textbf{62}(2011), 641-650.
  • Stieglitz, M., Tietz, H., \textit{Matrix transformationen von folgenraumen eine ergebnisubersict,} Math. Z., \textbf{154}(1977), 1-16.
  • Tripathy, B.C., {\em Matrix transformation between some classes of sequences}, J. Math. Anal. Appl., \textbf{2}(1997), 448-450.
  • Tu\u{g}, O., Ba\c{s}ar, F., {\em On the domain of N\"{o}rlund mean in the spaces of null and convergent sequences}, TWMS J. Pure Appl. Math., \textbf{7(1)}(2016), 76-87.
  • Tu\u{g}, O., Ba\c{s}ar, F., {\em On the spaces of N\"{o}rlund almost null and N\"{o}rlund almost convergent sequences}, Filomat, \textbf{30(3)}(2016), 773-783.
  • Wilansky, A., Summability through Functional Analysis, North-HollandMathematics Studies 85, Amsterdam-Newyork-Oxford, 1984.
Toplam 35 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Hacer Bilgin Ellidokuzoğlu

Serkan Demiriz

Yayımlanma Tarihi 29 Aralık 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 10

Kaynak Göster

APA Bilgin Ellidokuzoğlu, H., & Demiriz, S. (2018). Some Algebraic and Topological Properties of New Lucas Difference Sequence Spaces. Turkish Journal of Mathematics and Computer Science, 10, 144-152.
AMA Bilgin Ellidokuzoğlu H, Demiriz S. Some Algebraic and Topological Properties of New Lucas Difference Sequence Spaces. TJMCS. Aralık 2018;10:144-152.
Chicago Bilgin Ellidokuzoğlu, Hacer, ve Serkan Demiriz. “Some Algebraic and Topological Properties of New Lucas Difference Sequence Spaces”. Turkish Journal of Mathematics and Computer Science 10, Aralık (Aralık 2018): 144-52.
EndNote Bilgin Ellidokuzoğlu H, Demiriz S (01 Aralık 2018) Some Algebraic and Topological Properties of New Lucas Difference Sequence Spaces. Turkish Journal of Mathematics and Computer Science 10 144–152.
IEEE H. Bilgin Ellidokuzoğlu ve S. Demiriz, “Some Algebraic and Topological Properties of New Lucas Difference Sequence Spaces”, TJMCS, c. 10, ss. 144–152, 2018.
ISNAD Bilgin Ellidokuzoğlu, Hacer - Demiriz, Serkan. “Some Algebraic and Topological Properties of New Lucas Difference Sequence Spaces”. Turkish Journal of Mathematics and Computer Science 10 (Aralık 2018), 144-152.
JAMA Bilgin Ellidokuzoğlu H, Demiriz S. Some Algebraic and Topological Properties of New Lucas Difference Sequence Spaces. TJMCS. 2018;10:144–152.
MLA Bilgin Ellidokuzoğlu, Hacer ve Serkan Demiriz. “Some Algebraic and Topological Properties of New Lucas Difference Sequence Spaces”. Turkish Journal of Mathematics and Computer Science, c. 10, 2018, ss. 144-52.
Vancouver Bilgin Ellidokuzoğlu H, Demiriz S. Some Algebraic and Topological Properties of New Lucas Difference Sequence Spaces. TJMCS. 2018;10:144-52.