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

Year 2017, Volume: 38 Supplement Issue 4, 11 - 25, 08.12.2017

Mustafa Cemil Bişgin

https://doi.org/10.17776/csj.363211
https://izlik.org/JA84MM76FJ

Abstract

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

Keywords

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

References

  • [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)

Year 2017, Volume: 38 Supplement Issue 4, 11 - 25, 08.12.2017

Mustafa Cemil Bişgin

https://doi.org/10.17776/csj.363211
https://izlik.org/JA84MM76FJ

Abstract

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

Keywords

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

References

  • [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.
There are 17 citations in total.

Details

Journal Section Research Article
Authors

Mustafa Cemil Bişgin

Submission Date June 8, 2017
Acceptance Date October 13, 2017
Publication Date December 8, 2017
DOI https://doi.org/10.17776/csj.363211
IZ https://izlik.org/JA84MM76FJ
Published in Issue Year 2017 Volume: 38 Supplement Issue 4

Cite

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

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