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Genelleştirilmiş ağırlıklı B-Fark ortalama metoduyla tanımlanan hemen hemen yakınsak dizi uzayları için farklı bir yaklaşım

Yıl 2017, Cilt: 21 Sayı: 6, 1529 - 1536, 01.12.2017

Gülsen Kılınç Murat Candan

https://doi.org/10.16984/saufenbilder.321886
Cited By: 3

Öz

Bu çalışmada, B-fark matrisi ile genelleştirilmiş ağırlıklı ortalama metodu
yardımıyla inşa edilen   ve  dizi
uzaylarını tanımlandı. Bu uzaylar, genelleştirilmiş ağırlıklı -fark ortalamaları sırasıyla  ve  uzaylarında olan dizilerin uzayıdır.  ve  uzaylarının - ve -dualleri elde edildi. Ayrıca,  herhangi bir dizi uzayı olmak üzere  ve  sonsuz matrisleri karakterize edildi. 

Anahtar Kelimeler

matris dönüşümleri dizi uzayları bir dizi uzayının matris alanı dual uzaylar

Kaynakça

  • [1] B. Choudhary and S. Nanda, “Functional Analysis with applications,” John Wiley and Sons, New Delhi, I ̇ndia, 1989.
  • [2] G. G. Lorentz, “A contribution to the theory of divergent sequences,” Acta Mathematica, vol. 80, pp. 167-190, 1948.
  • [3] H. Kızmaz, “On certain sequence spaces,” Canad. Math. Bull. Vol.24, no.2, pp.169-176, 1981.
  • [4] M. Kirisçi, “Almost convergence and generalized weighted mean,” AIP Conf. Proc, vol. 1470, pp. 191–194, 2012.
  • [5] F. Başar and M. Kirisçi, “Almost convergence and generalized difference matrix,” Comput. Math. Appl., vol. 11, no. 1, pp. 51–63, 2000.
  • [6] K. Kayaduman and M. Şengönül, “On the Riesz almost convergent sequence space,” Abstr. Appl. Anal. Vol. 2012, article ID: 691694, 18 pages.
  • [7] M. Candan, “Almost convergence and double sequential band matrix,” Acta Math. Scientia, vol. 34, no. 2, pp. 354–366, 2014.
  • [8] D. Butkovic, H. Kraljevic and N. Sarapa “ on the almost convergence,” in Functional analysis, II, Lecture Notes in Mathematics, vol. 1242, 396417, Springer, Berlin, Germany, 1987.
  • [9] M. Kirisçi, “Almost convergence and generalized weighted mean II,” J. Ineq. and Appl, vol.1, no.93, 13 pages, 2014.
  • [10] H. Polat, V. Karakaya and N. Şimşek, “Difference sequence space reproduced by using a generalized weighted mean,” Applied Mathematics Letters, vol. 24, pp. 608–614, 2011.
  • [11] A. Karaisa and F.Başar, “Some new paranormed sequence spaces and core theorems,” AIP Conf. Proc. Vol. 1611, pp. 380–391, 2014.
  • [12] A. Karaisa and F. Özger, “Almost difference sequence spaces reproduced by using a generalized weighted mean,” J. Comput. Anal. and Appl., vol. 19, no. 1, pp. 27–38, 2015.
  • [13] K. Kayaduman and M. Şengönül, The space of Cesaro almost convergent sequence and core theorems,” Acta Mathematica Scientia, vol. 6, pp. 2265–2278, 2012.
  • [14] A. M. Jarrah and E. Malkowsky, “BK- spaces, bases and linear operators,” Ren. Circ. Mat. Palermo, vol. 2, no. 52, pp. 177–191, 1990.
  • [15] J. A. Sıddıqi, “Infinite matrices summing every almost periodic sequences,” Pacific J. Math, vol. 39, no. 1, pp. 235–251, 1971.
  • [16] F. Başar, “Summability Theory and Its Applications,” Bentham Science Publishers e-books, Monographs, xi+405 pp, ISB:978-1-60805-252-3, I ̇stanbul, (2012).
  • [17] J. P. Duran, “Infinite matrices and almost convergence,” Math. Z. Vol.128, pp.75-83, 1972.
  • [18] E. Öztürk, “On strongly regular dual summability methods,” Commun. Fac. Sci. Univ. Ank. Ser. A_1 Math. Stat., vol.32, p. 1-5, 1983.
  • [19] J. P. King, “Almost summable sequences,” Proc. Amer. Math. Soc. vol. 17, pp. 1219–1225, 1966.
  • [20] F. Basar and İ. Solak, “Almost-coercive matrix transformations,” Rend. Mat. Appl. vol. 7, no.11, pp. 249–256, 1991.
  • [21] F. Başar, “f-conservative matrix sequences” Tamkang J. Math, vol. 22, no. 2, pp. 205–212, 1991.
  • [22] F. Başar and R. Çolak, “Almost-conserva- tive matrix transformations,” Turkish J. Math, vol. 13, no.3, pp. 91- 100, 1989.
  • [23] F. Başar, “Strongly-conservative sequence to series matrix transformations,” Erc. Üni. Fen Bil. Derg. vol. 5, no.12, pp. 888–893, 1989.
  • [24] M. Candan and K. Kayaduman, “Almost Convergent sequence space Reproduced By Generalized Fibonacci Matrix and Fibonacci Core,” British J. Math. Comput. Sci, (Yayın No: 2002714), Doi: 10.9734/BJMCS/2015/15923.
  • [25] M. Candan, “Domain of Double Sequential Band Matrix in the Spaces of Convergent and Null Sequences,” Advanced in Difference Equations, vol.1, pp. 1-18, Yayın No: 2280631, 2014.
  • [26] M. Candan and A. Güneş, “Paranormed sequence spaces of Non Absolute Type Founded Using Generalized Difference Matrix,” Proceedings of the National Academy of Sciences; India Section A: Physical Sciences, vol. 85, no.2, pp. 269- 276, Yayın No:20038692014, Doi: 10.1007/s40010-015-0204-6, 2014.
  • [27] M. Candan, “A new Perspective On Paranormed Riesz sequence space of Non Absolute Type,” Global Journal of Mathematical Analysis, vol.3, no. 4, pp. 150–163, Doi: 1

A different approach for almost sequence spaces defined by a generalized weighted means

Yıl 2017, Cilt: 21 Sayı: 6, 1529 - 1536, 01.12.2017

Gülsen Kılınç Murat Candan

https://doi.org/10.16984/saufenbilder.321886
Cited By: 3

Öz

In this study, we introduce   and  sequence spaces which consisting of all
the sequences whose generalized weighted -difference means are found
in  and  spaces utilising generalized weighted mean
and  -difference matrices. The -and the -duals of the spaces  and  are determined. At the same time, we have
characterized the infinite matrices  and , where  is any given sequence space. 

Anahtar Kelimeler

matrix transformations sequence spaces matrix domain of a sequence space dual spaces

Kaynakça

  • [1] B. Choudhary and S. Nanda, “Functional Analysis with applications,” John Wiley and Sons, New Delhi, I ̇ndia, 1989.
  • [2] G. G. Lorentz, “A contribution to the theory of divergent sequences,” Acta Mathematica, vol. 80, pp. 167-190, 1948.
  • [3] H. Kızmaz, “On certain sequence spaces,” Canad. Math. Bull. Vol.24, no.2, pp.169-176, 1981.
  • [4] M. Kirisçi, “Almost convergence and generalized weighted mean,” AIP Conf. Proc, vol. 1470, pp. 191–194, 2012.
  • [5] F. Başar and M. Kirisçi, “Almost convergence and generalized difference matrix,” Comput. Math. Appl., vol. 11, no. 1, pp. 51–63, 2000.
  • [6] K. Kayaduman and M. Şengönül, “On the Riesz almost convergent sequence space,” Abstr. Appl. Anal. Vol. 2012, article ID: 691694, 18 pages.
  • [7] M. Candan, “Almost convergence and double sequential band matrix,” Acta Math. Scientia, vol. 34, no. 2, pp. 354–366, 2014.
  • [8] D. Butkovic, H. Kraljevic and N. Sarapa “ on the almost convergence,” in Functional analysis, II, Lecture Notes in Mathematics, vol. 1242, 396417, Springer, Berlin, Germany, 1987.
  • [9] M. Kirisçi, “Almost convergence and generalized weighted mean II,” J. Ineq. and Appl, vol.1, no.93, 13 pages, 2014.
  • [10] H. Polat, V. Karakaya and N. Şimşek, “Difference sequence space reproduced by using a generalized weighted mean,” Applied Mathematics Letters, vol. 24, pp. 608–614, 2011.
  • [11] A. Karaisa and F.Başar, “Some new paranormed sequence spaces and core theorems,” AIP Conf. Proc. Vol. 1611, pp. 380–391, 2014.
  • [12] A. Karaisa and F. Özger, “Almost difference sequence spaces reproduced by using a generalized weighted mean,” J. Comput. Anal. and Appl., vol. 19, no. 1, pp. 27–38, 2015.
  • [13] K. Kayaduman and M. Şengönül, The space of Cesaro almost convergent sequence and core theorems,” Acta Mathematica Scientia, vol. 6, pp. 2265–2278, 2012.
  • [14] A. M. Jarrah and E. Malkowsky, “BK- spaces, bases and linear operators,” Ren. Circ. Mat. Palermo, vol. 2, no. 52, pp. 177–191, 1990.
  • [15] J. A. Sıddıqi, “Infinite matrices summing every almost periodic sequences,” Pacific J. Math, vol. 39, no. 1, pp. 235–251, 1971.
  • [16] F. Başar, “Summability Theory and Its Applications,” Bentham Science Publishers e-books, Monographs, xi+405 pp, ISB:978-1-60805-252-3, I ̇stanbul, (2012).
  • [17] J. P. Duran, “Infinite matrices and almost convergence,” Math. Z. Vol.128, pp.75-83, 1972.
  • [18] E. Öztürk, “On strongly regular dual summability methods,” Commun. Fac. Sci. Univ. Ank. Ser. A_1 Math. Stat., vol.32, p. 1-5, 1983.
  • [19] J. P. King, “Almost summable sequences,” Proc. Amer. Math. Soc. vol. 17, pp. 1219–1225, 1966.
  • [20] F. Basar and İ. Solak, “Almost-coercive matrix transformations,” Rend. Mat. Appl. vol. 7, no.11, pp. 249–256, 1991.
  • [21] F. Başar, “f-conservative matrix sequences” Tamkang J. Math, vol. 22, no. 2, pp. 205–212, 1991.
  • [22] F. Başar and R. Çolak, “Almost-conserva- tive matrix transformations,” Turkish J. Math, vol. 13, no.3, pp. 91- 100, 1989.
  • [23] F. Başar, “Strongly-conservative sequence to series matrix transformations,” Erc. Üni. Fen Bil. Derg. vol. 5, no.12, pp. 888–893, 1989.
  • [24] M. Candan and K. Kayaduman, “Almost Convergent sequence space Reproduced By Generalized Fibonacci Matrix and Fibonacci Core,” British J. Math. Comput. Sci, (Yayın No: 2002714), Doi: 10.9734/BJMCS/2015/15923.
  • [25] M. Candan, “Domain of Double Sequential Band Matrix in the Spaces of Convergent and Null Sequences,” Advanced in Difference Equations, vol.1, pp. 1-18, Yayın No: 2280631, 2014.
  • [26] M. Candan and A. Güneş, “Paranormed sequence spaces of Non Absolute Type Founded Using Generalized Difference Matrix,” Proceedings of the National Academy of Sciences; India Section A: Physical Sciences, vol. 85, no.2, pp. 269- 276, Yayın No:20038692014, Doi: 10.1007/s40010-015-0204-6, 2014.
  • [27] M. Candan, “A new Perspective On Paranormed Riesz sequence space of Non Absolute Type,” Global Journal of Mathematical Analysis, vol.3, no. 4, pp. 150–163, Doi: 1
Toplam 27 adet kaynakça vardır.

Ayrıntılar

Bölüm Araştırma Makalesi
Yazarlar

Gülsen Kılınç

Murat Candan

Yayımlanma Tarihi 1 Aralık 2017
Gönderilme Tarihi 16 Haziran 2017
Kabul Tarihi 17 Ekim 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 21 Sayı: 6

Kaynak Göster

APA Kılınç, G., & Candan, M. (2017). A different approach for almost sequence spaces defined by a generalized weighted means. Sakarya University Journal of Science, 21(6), 1529-1536. https://doi.org/10.16984/saufenbilder.321886
AMA Kılınç G, Candan M. A different approach for almost sequence spaces defined by a generalized weighted means. SAUJS. Aralık 2017;21(6):1529-1536. doi:10.16984/saufenbilder.321886
Chicago Kılınç, Gülsen, ve Murat Candan. “A Different Approach for Almost Sequence Spaces Defined by a Generalized Weighted Means”. Sakarya University Journal of Science 21, sy. 6 (Aralık 2017): 1529-36. https://doi.org/10.16984/saufenbilder.321886.
EndNote Kılınç G, Candan M (01 Aralık 2017) A different approach for almost sequence spaces defined by a generalized weighted means. Sakarya University Journal of Science 21 6 1529–1536.
IEEE G. Kılınç ve M. Candan, “A different approach for almost sequence spaces defined by a generalized weighted means”, SAUJS, c. 21, sy. 6, ss. 1529–1536, 2017, doi: 10.16984/saufenbilder.321886.
ISNAD Kılınç, Gülsen - Candan, Murat. “A Different Approach for Almost Sequence Spaces Defined by a Generalized Weighted Means”. Sakarya University Journal of Science 21/6 (Aralık 2017), 1529-1536. https://doi.org/10.16984/saufenbilder.321886.
JAMA Kılınç G, Candan M. A different approach for almost sequence spaces defined by a generalized weighted means. SAUJS. 2017;21:1529–1536.
MLA Kılınç, Gülsen ve Murat Candan. “A Different Approach for Almost Sequence Spaces Defined by a Generalized Weighted Means”. Sakarya University Journal of Science, c. 21, sy. 6, 2017, ss. 1529-36, doi:10.16984/saufenbilder.321886.
Vancouver Kılınç G, Candan M. A different approach for almost sequence spaces defined by a generalized weighted means. SAUJS. 2017;21(6):1529-36.

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 Kapak Resmi İndir

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