A Note on the Sequence Space

Bu çalışmada, Binom ve genelleştirilmiş fark(ikili band) matrislerinin kompozisyonu ile türetilen , ( ) dizi uzayı tanımlandı ve , ( ) uzayının 1

?? ?,? (?) Dizi Uzayı Üzerine Bir Not

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 , ( ). Moreover, we determine -, - and -duals of the space , ( ). Lastly, we characterize of the space some matrix classes related to the space , ( )e ?? ?,? (?).

___

  • [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 ?? and ?∞ I. Inf. Sci., 2006; 176(10): 1450-1462.
  • [9]. Mursaleen M., Başar F., Altay B. On the Euler sequence spaces which include the spaces ?? and ?∞ 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 ? (?) -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 ?? and ?∞ 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.