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b_p^(r,s) (G) Dizi Uzayı Üzerine Bir Not

Yıl 2017, , 11 - 25, 08.12.2017

Mustafa Cemil Bişgin

https://doi.org/10.17776/csj.363211
Cited By: 2

Öz

Bu
çalışmada, Binom ve genelleştirilmiş fark(ikili band) matrislerinin
kompozisyonu ile türetilen



















 dizi uzayı tanımlandı ve

 uzayının

 durumlarında

 uzayına lineer olarak izomorfik olduğu
gösterildi. Ayrıca, bazı kapsama bağıntılarından bahsedildi ve

 uzayının Schauder bazı verildi. Bundan başka,

 uzayının

-,

- ve

-dualleri belirlendi. Son olarak,

 uzayı ile ilgili bazı matris sınıfları
karakterize edildi.



MKS: 40C05;40H05;46B45

Anahtar Kelimeler

Matris Dönüşümü Etki Alanı Schauder Bazı α- β- ve γ-Dualleri

Kaynakça

  • [1]. Choudhary B., Nanda S. Functional analysis with applications, Wiley, New Delhi,(1989).
  • [2]. Wilansky A. Summability through functional analysis, North-Holland Mathematics Studies, vol. 85. Elsevier, Amsterdam (1984).
  • [3]. Wang C-S., On norlund sequence spaces. Tamkang J. Math., 1978; 9: 269-274.
  • [4]. Ng P-N., Lee P-Y., Cesaro sequence spaces of non-absolute type. Comment. Math. (Prace Mat.), 1978; 20(2): 429-433.
  • [5]. Kızmaz H., On certain sequence spaces. Canad. Math. Bull., 1981; 24(2): 169-176.
  • [6]. Et M., On some difference sequence spaces. Turkish J. Math., 1993; 17: 18-24.
  • [7]. Altay B., Başar, F., Some Euler sequence spaces of non-absolute type. Ukr. Math. J., 2005; 57(1): 1-17.
  • [8]. Altay B., Başar, F., Mursaleen, M., On the Euler sequence spaces which include the spaces l_p and l_∞ I. Inf. Sci., 2006; 176(10): 1450-1462.
  • [9]. Mursaleen M., Başar F., Altay B. On the Euler sequence spaces which include the spaces l_p and l_∞ II. Nonlinear Anal., 2006; 65(3): 707-717.
  • [10]. Altay B., Polat H. On some new Euler difference sequence spaces. Southeast Asian Bull. Math., 2006; 30(2): 209-220.
  • [11]. Polat H., Başar F. Some Euler spaces of difference sequences of order m. Acta Math.Sci. Ser. B, Engl. Ed., 2007; 27B(2): 254-266.
  • [12]. Kara E.E., Başarır M. On compact operators and some Euler B^((m))-difference sequence spaces. J. Math. Anal. Appl., 2011; 379(2): 499-511.
  • [13]. Kirişçi M., Başar F. Some new sequence spaces derived by the domain of generalized difference matrix. Comput. Math. Appl., 2010; 60(5): 1299-1309.
  • [14]. Bişgin M.C. The Binomial sequence spaces of nonabsolute type. J. Inequal. Appl., 2016; 2016:309.
  • [15]. Bişgin M.C. The Binomial sequence spaces which include the spaces l_p and l_∞ and geometric properties. J. Inequal. Appl., 2016; 2016:304.
  • [16]. Jarrah A.M., Malkowsky E., BK-spaces, bases and linear operators. Rend. Circ. Mat. Palermo, 1998; 52(2): 177-191.
  • [17]. Stieglitz M., Tietz H., Matrix Transformationen von Folgenräumen eine ergebnisübersicht. Math. Z., 1977; 154: 1-16.

A Note on the Sequence Space b_p^(r,s) (G)

Yıl 2017, , 11 - 25, 08.12.2017

Mustafa Cemil Bişgin

https://doi.org/10.17776/csj.363211
Cited By: 2

Öz

In this study, we define the sequence space



















 derived by the composition of the Binomial
matrix and generalized difference(double band) matrix and show that the space

 is linearly isomorphic to the space

, where

. Furthermore, we mention some
inclusion relations and give Schauder basis of the space

. Moreover, we determine

-,

- and

-duals of the space

. Lastly, we characterize some
matrix classes related to the space

.



MSC:
40C05;40H05;46B45

Anahtar Kelimeler

Matrix Transformation Matrix Domain Schauder Basis α- β- and γ-Duals

Kaynakça

  • [1]. Choudhary B., Nanda S. Functional analysis with applications, Wiley, New Delhi,(1989).
  • [2]. Wilansky A. Summability through functional analysis, North-Holland Mathematics Studies, vol. 85. Elsevier, Amsterdam (1984).
  • [3]. Wang C-S., On norlund sequence spaces. Tamkang J. Math., 1978; 9: 269-274.
  • [4]. Ng P-N., Lee P-Y., Cesaro sequence spaces of non-absolute type. Comment. Math. (Prace Mat.), 1978; 20(2): 429-433.
  • [5]. Kızmaz H., On certain sequence spaces. Canad. Math. Bull., 1981; 24(2): 169-176.
  • [6]. Et M., On some difference sequence spaces. Turkish J. Math., 1993; 17: 18-24.
  • [7]. Altay B., Başar, F., Some Euler sequence spaces of non-absolute type. Ukr. Math. J., 2005; 57(1): 1-17.
  • [8]. Altay B., Başar, F., Mursaleen, M., On the Euler sequence spaces which include the spaces l_p and l_∞ I. Inf. Sci., 2006; 176(10): 1450-1462.
  • [9]. Mursaleen M., Başar F., Altay B. On the Euler sequence spaces which include the spaces l_p and l_∞ II. Nonlinear Anal., 2006; 65(3): 707-717.
  • [10]. Altay B., Polat H. On some new Euler difference sequence spaces. Southeast Asian Bull. Math., 2006; 30(2): 209-220.
  • [11]. Polat H., Başar F. Some Euler spaces of difference sequences of order m. Acta Math.Sci. Ser. B, Engl. Ed., 2007; 27B(2): 254-266.
  • [12]. Kara E.E., Başarır M. On compact operators and some Euler B^((m))-difference sequence spaces. J. Math. Anal. Appl., 2011; 379(2): 499-511.
  • [13]. Kirişçi M., Başar F. Some new sequence spaces derived by the domain of generalized difference matrix. Comput. Math. Appl., 2010; 60(5): 1299-1309.
  • [14]. Bişgin M.C. The Binomial sequence spaces of nonabsolute type. J. Inequal. Appl., 2016; 2016:309.
  • [15]. Bişgin M.C. The Binomial sequence spaces which include the spaces l_p and l_∞ and geometric properties. J. Inequal. Appl., 2016; 2016:304.
  • [16]. Jarrah A.M., Malkowsky E., BK-spaces, bases and linear operators. Rend. Circ. Mat. Palermo, 1998; 52(2): 177-191.
  • [17]. Stieglitz M., Tietz H., Matrix Transformationen von Folgenräumen eine ergebnisübersicht. Math. Z., 1977; 154: 1-16.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Bölüm Natural Sciences
Yazarlar

Mustafa Cemil Bişgin

Yayımlanma Tarihi 8 Aralık 2017
Gönderilme Tarihi 8 Haziran 2017
Kabul Tarihi 13 Ekim 2017
Yayımlandığı Sayı Yıl 2017

Kaynak Göster

APA Bişgin, M. C. (2017). A Note on the Sequence Space b_p^(r,s) (G). Cumhuriyet Science Journal, 38(4), 11-25. https://doi.org/10.17776/csj.363211

Cited By

New Integrated and Differentiated Sequence Spaces ∫ b_p^(r,s) and db_p^(r,s)
Sakarya University Journal of Science
https://doi.org/10.16984/saufenbilder.1529080
Some Notes on the New Sequence Space b_p^(r,s) (D)
Gazi University Journal of Science
https://doi.org/10.35378/gujs.522691