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DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES

Yıl 2017, Cilt: 5 Sayı: 2, 260 - 267, 15.10.2017

Öz

In this paper we show that completeness and barrelledness of a normed space can be characterized by means of sequence spaces obtained by a sequence in a normed space and difference matrix method. Other related results are established.

Kaynakça

  • [1] Aizpuru, A. and Perez-Fernandez, F. J., Characterizations of series in Banach spaces, Acta Math. Univ. Comenian., 58 (1999), No. 2, 337–344.
  • [2] Aizpuru, A. and Perez-Fernandez, F. J., Sequence spaces associated to a series in a Banach space (sequence spaces associated to a series), Indian J. pure appl. Math., 33 (2002), No. 9, 1317–1329.
  • [3] F.Albiac, N. J.Kalton, Topics in Banach Spaces Theory, Springer-Verlag, New York (2006).
  • [4] B. Altay, F. Basar Certain topological properties and duals of the domain of a triangle matrix in a sequence space, J. Math. Anal. Appl. 336 (2007), no. 2, 632–645.
  • [5] F. Basar, B. Altay, On the space of sequences of p-bounded variation and related matrix mappings, (English, Ukrainian summary) Ukrain. Mat. Zh., 55(1) (2003), 108–118; reprinted in Ukrainian Math. J., 55(1) (2003), 136–147.
  • [6] C.A. Bektas, R. Colak, On some generalized difference sequence spaces, Thai J. Math., 3(1) (2005), 83–98.
  • [7] C. Bessaga, A. Pelczynski, On bases and unconditional convergence of series in Banach spaces, Stud. Math., 17 (1958), 151–164.
  • [8] J. Diestel, Sequences and Series in Banach Spaces, Springer-Verlag, New York (1984).
  • [9] M. Et and R. Colak, On some generalized difference sequence spaces, Soochow J. of Math., 21(4) (1995), 377–386.
  • [10] R. Kama, B. Altay, F. Basar, On the domains of backward difference matrix and the spaces of convergence of a series, preprint.
  • [11] R. Kama, B. Altay, Some sequence spaces and completeness of normed spaces, Creat. Math. Inform., to appear.
  • [12] V. Karakaya, E. Sava ̧s, H. Polat, Some paranormed Euler sequence spaces of difference sequences of order m, Mathematica Slovaca, 63(4) (2013), 849–862.
  • [13] H. Kızmaz, On certain sequence spaces, Canad. Math. Bull., 24(2) (1981), 169–175.
  • [14] E. Malkowsky, Mursaleen and Qamaruddin, Generalized sets of difference sequences, their duals and matrix transformations, Advances in Sequence Spaces and Applications, Narosa, New Delhi, (1999), 68-83.
  • [15] C.W. McArthur, On relationships amongst certain spaces of sequences in an arbitrary Banach space, Canad. J. Math., 8 (1956), 192–197.
  • [16] F.J. Perez-Fernandez, F. Benıtez-Trujillo, A. Aizpuru, Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series, Czechoslovak Math. J., 50 (2000), no. 125, 889–896.
Yıl 2017, Cilt: 5 Sayı: 2, 260 - 267, 15.10.2017

Öz

Kaynakça

  • [1] Aizpuru, A. and Perez-Fernandez, F. J., Characterizations of series in Banach spaces, Acta Math. Univ. Comenian., 58 (1999), No. 2, 337–344.
  • [2] Aizpuru, A. and Perez-Fernandez, F. J., Sequence spaces associated to a series in a Banach space (sequence spaces associated to a series), Indian J. pure appl. Math., 33 (2002), No. 9, 1317–1329.
  • [3] F.Albiac, N. J.Kalton, Topics in Banach Spaces Theory, Springer-Verlag, New York (2006).
  • [4] B. Altay, F. Basar Certain topological properties and duals of the domain of a triangle matrix in a sequence space, J. Math. Anal. Appl. 336 (2007), no. 2, 632–645.
  • [5] F. Basar, B. Altay, On the space of sequences of p-bounded variation and related matrix mappings, (English, Ukrainian summary) Ukrain. Mat. Zh., 55(1) (2003), 108–118; reprinted in Ukrainian Math. J., 55(1) (2003), 136–147.
  • [6] C.A. Bektas, R. Colak, On some generalized difference sequence spaces, Thai J. Math., 3(1) (2005), 83–98.
  • [7] C. Bessaga, A. Pelczynski, On bases and unconditional convergence of series in Banach spaces, Stud. Math., 17 (1958), 151–164.
  • [8] J. Diestel, Sequences and Series in Banach Spaces, Springer-Verlag, New York (1984).
  • [9] M. Et and R. Colak, On some generalized difference sequence spaces, Soochow J. of Math., 21(4) (1995), 377–386.
  • [10] R. Kama, B. Altay, F. Basar, On the domains of backward difference matrix and the spaces of convergence of a series, preprint.
  • [11] R. Kama, B. Altay, Some sequence spaces and completeness of normed spaces, Creat. Math. Inform., to appear.
  • [12] V. Karakaya, E. Sava ̧s, H. Polat, Some paranormed Euler sequence spaces of difference sequences of order m, Mathematica Slovaca, 63(4) (2013), 849–862.
  • [13] H. Kızmaz, On certain sequence spaces, Canad. Math. Bull., 24(2) (1981), 169–175.
  • [14] E. Malkowsky, Mursaleen and Qamaruddin, Generalized sets of difference sequences, their duals and matrix transformations, Advances in Sequence Spaces and Applications, Narosa, New Delhi, (1999), 68-83.
  • [15] C.W. McArthur, On relationships amongst certain spaces of sequences in an arbitrary Banach space, Canad. J. Math., 8 (1956), 192–197.
  • [16] F.J. Perez-Fernandez, F. Benıtez-Trujillo, A. Aizpuru, Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series, Czechoslovak Math. J., 50 (2000), no. 125, 889–896.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Articles
Yazarlar

Ramazan Kama

Bilal Altay

Yayımlanma Tarihi 15 Ekim 2017
Gönderilme Tarihi 4 Mayıs 2017
Kabul Tarihi 17 Mayıs 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 5 Sayı: 2

Kaynak Göster

APA Kama, R., & Altay, B. (2017). DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES. Konuralp Journal of Mathematics, 5(2), 260-267.
AMA Kama R, Altay B. DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES. Konuralp J. Math. Ekim 2017;5(2):260-267.
Chicago Kama, Ramazan, ve Bilal Altay. “DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES”. Konuralp Journal of Mathematics 5, sy. 2 (Ekim 2017): 260-67.
EndNote Kama R, Altay B (01 Ekim 2017) DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES. Konuralp Journal of Mathematics 5 2 260–267.
IEEE R. Kama ve B. Altay, “DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES”, Konuralp J. Math., c. 5, sy. 2, ss. 260–267, 2017.
ISNAD Kama, Ramazan - Altay, Bilal. “DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES”. Konuralp Journal of Mathematics 5/2 (Ekim 2017), 260-267.
JAMA Kama R, Altay B. DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES. Konuralp J. Math. 2017;5:260–267.
MLA Kama, Ramazan ve Bilal Altay. “DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES”. Konuralp Journal of Mathematics, c. 5, sy. 2, 2017, ss. 260-7.
Vancouver Kama R, Altay B. DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES. Konuralp J. Math. 2017;5(2):260-7.
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