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

Year 2017, , 1529 - 1536, 01.12.2017
https://doi.org/10.16984/saufenbilder.321886

Abstract

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. 

References

  • [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

Year 2017, , 1529 - 1536, 01.12.2017
https://doi.org/10.16984/saufenbilder.321886

Abstract

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. 

References

  • [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
There are 27 citations in total.

Details

Journal Section Research Articles
Authors

Gülsen Kılınç

Murat Candan

Publication Date December 1, 2017
Submission Date June 16, 2017
Acceptance Date October 17, 2017
Published in Issue Year 2017

Cite

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. December 2017;21(6):1529-1536. doi:10.16984/saufenbilder.321886
Chicago Kılınç, Gülsen, and Murat Candan. “A Different Approach for Almost Sequence Spaces Defined by a Generalized Weighted Means”. Sakarya University Journal of Science 21, no. 6 (December 2017): 1529-36. https://doi.org/10.16984/saufenbilder.321886.
EndNote Kılınç G, Candan M (December 1, 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 and M. Candan, “A different approach for almost sequence spaces defined by a generalized weighted means”, SAUJS, vol. 21, no. 6, pp. 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 (December 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 and Murat Candan. “A Different Approach for Almost Sequence Spaces Defined by a Generalized Weighted Means”. Sakarya University Journal of Science, vol. 21, no. 6, 2017, pp. 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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