Araştırma Makalesi
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Fark Seri Uzayları ve Matris Dönüşümleri

Yıl 2020, , 137 - 143, 18.06.2020
https://doi.org/10.46810/tdfd.726322

Öz

Bu çalışmada, Cesàro ortalaması ve fark operatörü kullanılarak yeni bir |C_α |_p (∇) seri uzayı tanımlanmıştır. Bu yeni |C_α |_p (∇) uzayının bir BK- uzayı olduğu ve Schauder bazına sahip olduğu gösterilmiştir. Ayrıca, |C_α |_p (∇) uzayının α, β, and γ- dualleri hesaplanmış ve |C_α |_p (∇) uzayından X={l_∞,c,c_0} uzayına matris dönüşümleri karakterize edilmiştir.

Proje Numarası

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Kaynakça

  • [1] Aydın C, Başar F. Some new difference sequence spaces. Appl. Math. Comput. 2004;157(3):677–693.
  • [2] Başar F, Altay B. On the space of sequences of p-bounded variation and related matrix mappings. Ukrainian Math. J. 2003;55(1):136–147.
  • [3] Çolak R, Et M. On some generalized difference sequence spaces and related matrix transformations. Hokkaido Math. J. 1997;26(3):483–492.
  • [4] Demiriz S, Çakan C. Some topological and geometrical properties of a new difference sequence space. Abstract and Applied Analysis. 2011; Volume 2011, Article ID 213878: 14 pages, doi:10.1155/2011/213878.
  • [5] Demiriz S, Çakan C. Some new paranormed sequence spaces and α−core of a sequence. Pure and Applied Mathematics Letters. 2016; Volume 2016: 32-45.
  • [6] Duyar O, Demiriz S, Özdemir O. On some new generalized difference sequence spaces of nonabsolute type. Journal of Mathematics. 2014;
  • [7] Ellidokuzoğlu HB, Demiriz S. Euler-Riesz Difference Sequence Spaces. Turk. J. Math. Comput. Sci. 2017;7:63-72.
  • [8] Hazar GC, Sarıgöl MA. On absolute Nörlund spaces and matrix operators. Acta Math. Sin. (Engl. Ser.). 2018;34(5):812-826.
  • [9] Hazar Güleç GC, Sarıgöl MA. Compact and Matrix Operators on the Space |C,−1|k. J. Comput. Anal. Appl. 2018;25(6):1014-1024.
  • [10] Hazar Güleç GC. Compact Matrix Operators on Absolute Cesàro Spaces. Numer. Func. Anal. Opt. 2020;41(1):1-15.
  • [11] Hazar Güleç GC. Characterization of some classes of compact and matrix operators on the sequence spaces of Cesàro means. Operator and Matrices. 2019;13(3):809-822.
  • [12] İlkhan M, Kara EE. A new Banach space defined by Euler totient matrix operator. Operator Matrices. 2019;13(2):527-544.
  • [13] İlkhan M, Demiriz S, Kara EE. A new paranormed sequence space defined by Euler totient matrix. Karaelmas Sci. Eng. J. 2019; 9(2).
  • [14] Sarıgöl MA. On difference sequence spaces. J. Karadeniz Tech. Univ. Fac. Arts Sci. Ser. Math.-Phys. 1987;10:63-71.
  • [15] Sarıgöl MA. Matrix transformations on fields of absolute weighted mean summability. Studia Sci. Math. Hungar. 2011;48(3):331-341.
  • [16] Sarıgöl MA. Spaces of series summable by absolute Cesàro and matrix operators. Comm. Math Appl. 2016;7(1):11-22.
  • [17] Sezer SA, Çanak İ. On a Tauberian theorem for the weighted mean method of summability. Kuwait J. Sci. 2015;42:1-9.
  • [18] Kizmaz H. On certain sequence spaces. Canad. Math. Bull. 1981;24(2):169–176.
  • [19] Orhan C. Matrix transformations on Cesàro difference sequence spaces. Comm. Fac. Sci. Univ. Ankara Ser. A1 1984;33(1):1–8.
  • [20] Polat H, Altay B. On some new Euler difference sequence spaces. Southeast Asian Bull. Math. 2006;30:209–220.
  • [21] Flett TM. On an extension of absolute summability and some theorems of Littlewood and Paley. Proc. London Math. Soc. 1957;7:113-141.
  • [22] Wilansky A. Summability Through Functional Analysis. North-Holland Mathematical Studies. vol. 85. Elsevier Science Publisher; 1984.
  • [23] Stieglitz M, Tietz H. Matrixtransformationen von folgenraumen eine ergebnisüberischt. Math Z. 1977;154:1-16.
  • [24] Sarıgöl MA. Extension of Mazhar’s theorem on summability factors. Kuwait J. Sci. 2015;42(3):28-35.
  • [25] Maddox IJ. Elements of functional analysis. Cambridge University Press. London, New York; 1970.

Difference Series Spaces and Matrix Transformations

Yıl 2020, , 137 - 143, 18.06.2020
https://doi.org/10.46810/tdfd.726322

Öz

This paper deals with new series space |C_α |_p (∇) introduced by using Cesàro means and difference operator. It is shown that this newly defined space |C_α |_p (∇) is a BK- space and has Schauder basis. Furthermore, the α, β, and γ-duals of |C_α |_p (∇) are computed and the characterizations of classes of matrix mappings from |C_α |_p (∇) to X={l_∞,c,c_0} are also given.

Destekleyen Kurum

-

Proje Numarası

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Kaynakça

  • [1] Aydın C, Başar F. Some new difference sequence spaces. Appl. Math. Comput. 2004;157(3):677–693.
  • [2] Başar F, Altay B. On the space of sequences of p-bounded variation and related matrix mappings. Ukrainian Math. J. 2003;55(1):136–147.
  • [3] Çolak R, Et M. On some generalized difference sequence spaces and related matrix transformations. Hokkaido Math. J. 1997;26(3):483–492.
  • [4] Demiriz S, Çakan C. Some topological and geometrical properties of a new difference sequence space. Abstract and Applied Analysis. 2011; Volume 2011, Article ID 213878: 14 pages, doi:10.1155/2011/213878.
  • [5] Demiriz S, Çakan C. Some new paranormed sequence spaces and α−core of a sequence. Pure and Applied Mathematics Letters. 2016; Volume 2016: 32-45.
  • [6] Duyar O, Demiriz S, Özdemir O. On some new generalized difference sequence spaces of nonabsolute type. Journal of Mathematics. 2014;
  • [7] Ellidokuzoğlu HB, Demiriz S. Euler-Riesz Difference Sequence Spaces. Turk. J. Math. Comput. Sci. 2017;7:63-72.
  • [8] Hazar GC, Sarıgöl MA. On absolute Nörlund spaces and matrix operators. Acta Math. Sin. (Engl. Ser.). 2018;34(5):812-826.
  • [9] Hazar Güleç GC, Sarıgöl MA. Compact and Matrix Operators on the Space |C,−1|k. J. Comput. Anal. Appl. 2018;25(6):1014-1024.
  • [10] Hazar Güleç GC. Compact Matrix Operators on Absolute Cesàro Spaces. Numer. Func. Anal. Opt. 2020;41(1):1-15.
  • [11] Hazar Güleç GC. Characterization of some classes of compact and matrix operators on the sequence spaces of Cesàro means. Operator and Matrices. 2019;13(3):809-822.
  • [12] İlkhan M, Kara EE. A new Banach space defined by Euler totient matrix operator. Operator Matrices. 2019;13(2):527-544.
  • [13] İlkhan M, Demiriz S, Kara EE. A new paranormed sequence space defined by Euler totient matrix. Karaelmas Sci. Eng. J. 2019; 9(2).
  • [14] Sarıgöl MA. On difference sequence spaces. J. Karadeniz Tech. Univ. Fac. Arts Sci. Ser. Math.-Phys. 1987;10:63-71.
  • [15] Sarıgöl MA. Matrix transformations on fields of absolute weighted mean summability. Studia Sci. Math. Hungar. 2011;48(3):331-341.
  • [16] Sarıgöl MA. Spaces of series summable by absolute Cesàro and matrix operators. Comm. Math Appl. 2016;7(1):11-22.
  • [17] Sezer SA, Çanak İ. On a Tauberian theorem for the weighted mean method of summability. Kuwait J. Sci. 2015;42:1-9.
  • [18] Kizmaz H. On certain sequence spaces. Canad. Math. Bull. 1981;24(2):169–176.
  • [19] Orhan C. Matrix transformations on Cesàro difference sequence spaces. Comm. Fac. Sci. Univ. Ankara Ser. A1 1984;33(1):1–8.
  • [20] Polat H, Altay B. On some new Euler difference sequence spaces. Southeast Asian Bull. Math. 2006;30:209–220.
  • [21] Flett TM. On an extension of absolute summability and some theorems of Littlewood and Paley. Proc. London Math. Soc. 1957;7:113-141.
  • [22] Wilansky A. Summability Through Functional Analysis. North-Holland Mathematical Studies. vol. 85. Elsevier Science Publisher; 1984.
  • [23] Stieglitz M, Tietz H. Matrixtransformationen von folgenraumen eine ergebnisüberischt. Math Z. 1977;154:1-16.
  • [24] Sarıgöl MA. Extension of Mazhar’s theorem on summability factors. Kuwait J. Sci. 2015;42(3):28-35.
  • [25] Maddox IJ. Elements of functional analysis. Cambridge University Press. London, New York; 1970.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

G. Canan H. Güleç 0000-0002-8825-5555

Proje Numarası -
Yayımlanma Tarihi 18 Haziran 2020
Yayımlandığı Sayı Yıl 2020

Kaynak Göster

APA H. Güleç, G. C. (2020). Difference Series Spaces and Matrix Transformations. Türk Doğa Ve Fen Dergisi, 9(1), 137-143. https://doi.org/10.46810/tdfd.726322
AMA H. Güleç GC. Difference Series Spaces and Matrix Transformations. TDFD. Haziran 2020;9(1):137-143. doi:10.46810/tdfd.726322
Chicago H. Güleç, G. Canan. “Difference Series Spaces and Matrix Transformations”. Türk Doğa Ve Fen Dergisi 9, sy. 1 (Haziran 2020): 137-43. https://doi.org/10.46810/tdfd.726322.
EndNote H. Güleç GC (01 Haziran 2020) Difference Series Spaces and Matrix Transformations. Türk Doğa ve Fen Dergisi 9 1 137–143.
IEEE G. C. H. Güleç, “Difference Series Spaces and Matrix Transformations”, TDFD, c. 9, sy. 1, ss. 137–143, 2020, doi: 10.46810/tdfd.726322.
ISNAD H. Güleç, G. Canan. “Difference Series Spaces and Matrix Transformations”. Türk Doğa ve Fen Dergisi 9/1 (Haziran 2020), 137-143. https://doi.org/10.46810/tdfd.726322.
JAMA H. Güleç GC. Difference Series Spaces and Matrix Transformations. TDFD. 2020;9:137–143.
MLA H. Güleç, G. Canan. “Difference Series Spaces and Matrix Transformations”. Türk Doğa Ve Fen Dergisi, c. 9, sy. 1, 2020, ss. 137-43, doi:10.46810/tdfd.726322.
Vancouver H. Güleç GC. Difference Series Spaces and Matrix Transformations. TDFD. 2020;9(1):137-43.