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On A New Almost Convergent Sequence Space Defined By The Matrix ∆_u^λ

Year 2020, , 321 - 329, 15.04.2020
https://doi.org/10.17714/gumusfenbil.639476

Abstract

In
this study, it is defined almost sequence spaces 
f(Λ ̂ ), f_0(Λ ̂ ) and fs(Λ ̂ ) as domain of the
matrix
∆_u^λ Some topological
properties of these spaces are investigated and determined 
β-,  γ- duals of aforementioned sequence space. Futhermore, it is
characterized the class of matrices 
(f(Λ ̂ ): μ)(fs(Λ ̂ ):μ),( μ:f(Λ ̂ )) and  ( μ:fs(Λ ̂), where μ is any given
sequence space. 

References

  • Başar, F., 1989. Strongly-conservative sequence to series matrix transformations, Erc. Üni. Fen Bil. Derg. 5, (12), 888–893.
  • Başar, F. and Çolak, R., 1989. Almost-conservative matrix transformations, Turkish J. Math, 13, (3), 91- 100.
  • Başar, F., 1991. f -conservative matrix sequences, Tamkang J. Math, 22, (2), 205–212..
  • Başar, F. and Solak, İ., 1991. Almost-coercive matrix transformations, Rend. Mat. Appl. 7, (11) 249–256.
  • Başar, F. and Kirişçi, M., 2011. Almost convergence and generalized difference matrix, Comput. Math. Appl. 61, 602-611.
  • Başar, F., 2012. Summability Theory and Its Applications, Bentham Science Publishers ebooks, Monographs, xi+405 pp, ISB:978-1-60805-252-3, İstanbul
  • Butkovic, D., Kraljevic, H. and Sarapa, H. N., 1987. On the almost convergence, in Functional analysis, II, Lecture Notes in Mathematics, 1242, 396417, (Springer, Berlin, Germany).
  • Candan, M., 2012. Domain of the double sequential band matrix in the classical sequence spaces, Journal of Inequalities and Applications 2012 (1), 2012:281, 15 pages.
  • Candan, M., 2014. Some New Sequence Spaces Derived from the Spaces of Bounded, Convergent and Null Sequences, International Journal of Modern Mathematical Sciences, 12(2), 74-87.
  • Candan, M., 2014. Domain of the double sequential band matrix in the spaces of convergent and null sequences, Advances in Difference Equations 2014:163, 18 pages.
  • Candan, M., 2014. Almost convergence and double sequential band matrix, Acta Math. Scientia, 34, (2), 354–366.
  • Candan, M. and Kayaduman, K., 2015. Almost Convergent sequence space Reproduced By Generalized Fibonacci Matrix and Fibonacci Core, British J. Math. Comput. Sci. 7, (2), 150-167.
  • Candan, M., 2018. A New Outlook for Almost Convergent Sequence Spaces, Cumhuriyet Sci. J. 39, (1), 34-46.
  • Duran, J. P., 1972. Infinite matrices and almost convergence, Math. Z. 128, 75-83.
  • Ganie, A. and Sheikh, N. A., 2013. On some new sequence spaces of non-absolute type and matrix transformations, Egyptian Mathematical Society, 21, 108-114.
  • Jarrah, A. M., and Malkowsky, E., 1990. BK- spaces, bases and linear operators, Ren. Circ. Mat. Palermo, 2, (52), 177–191.
  • Karaisa, A. and Özger, F., 2015. Almost difference sequence spaces reproduced by using a generalized weighted mean, J. Comput. Anal. and Appl. 19, (1), 27–38.
  • Kayaduman, K. and Şengönül, M.,(a) 2012. On the Riesz almost convergent sequence space, Abstr. Appl. Anal. 2012, article ID: 691694, 18 pages.
  • Kayaduman, K. and Şengönül, M., (b) 2012. The space of Cesaro almost convergent sequence and core theorems, Acta Mathematica Scientia, 6, 2265–2278.
  • King, J. P., 1966. Almost summable sequences, Proc. Amer. Math. Soc. 17, 1219 -1225.
  • Kirisçi, M., 2012. Almost convergence and generalized weighted mean, AIP Conf. Proc, 1470,191–194.
  • Kirisçi, M., 2014. Almost convergence and generalized weighted mean II, J.Ineq. and Appl., 1, 93, 13pages.
  • Lorentz, G. G.,1948. A contribution to the theory of divergent sequences, Acta Mathematica, 80, 167-190.
  • Móricz, F. and Rhoades, B. E., 1990. Some characterizations of almost convergence for single and double sequences. Publ. Inst. Math Nouv S`er, 48, (62), 61–68.
  • Öztürk, E.,1983. On strongly regular dual summability methods, Commun. Fac. Sci. Univ. Ank. Series: A_1, Math., Stat. 32, 1-5.
  • Sıddıqi, J. A., 1971. Infinite matrices summing every almost periodic sequences, Pacific J. Math, 39, (1), 235–251.

∆_u^λ Matrisi Yardımıyla Tanımlanan Yeni Bir Hemen Hemen Yakınsak Dizi Uzayı Üzerine

Year 2020, , 321 - 329, 15.04.2020
https://doi.org/10.17714/gumusfenbil.639476

Abstract

Bu
çalışmada
 ∆_u^λ matrisinin etki alanları olarak f(Λ ̂ ), f_0(Λ ̂ ) ve fs(Λ ̂ ) hemen hemen
yakınsak dizi uzayları tanımlandı. Bu uzayların bazı topolojik özellikleri
incelendi ve 
β-,  γ- dualleri belirlendi.
Ayrıca,
(f(Λ ̂ ): μ)(fs(Λ ̂ ):μ),( μ:f(Λ ̂ )) ve ( μ:fs(Λ ̂),  matris sınıfları karakterize edildi.

References

  • Başar, F., 1989. Strongly-conservative sequence to series matrix transformations, Erc. Üni. Fen Bil. Derg. 5, (12), 888–893.
  • Başar, F. and Çolak, R., 1989. Almost-conservative matrix transformations, Turkish J. Math, 13, (3), 91- 100.
  • Başar, F., 1991. f -conservative matrix sequences, Tamkang J. Math, 22, (2), 205–212..
  • Başar, F. and Solak, İ., 1991. Almost-coercive matrix transformations, Rend. Mat. Appl. 7, (11) 249–256.
  • Başar, F. and Kirişçi, M., 2011. Almost convergence and generalized difference matrix, Comput. Math. Appl. 61, 602-611.
  • Başar, F., 2012. Summability Theory and Its Applications, Bentham Science Publishers ebooks, Monographs, xi+405 pp, ISB:978-1-60805-252-3, İstanbul
  • Butkovic, D., Kraljevic, H. and Sarapa, H. N., 1987. On the almost convergence, in Functional analysis, II, Lecture Notes in Mathematics, 1242, 396417, (Springer, Berlin, Germany).
  • Candan, M., 2012. Domain of the double sequential band matrix in the classical sequence spaces, Journal of Inequalities and Applications 2012 (1), 2012:281, 15 pages.
  • Candan, M., 2014. Some New Sequence Spaces Derived from the Spaces of Bounded, Convergent and Null Sequences, International Journal of Modern Mathematical Sciences, 12(2), 74-87.
  • Candan, M., 2014. Domain of the double sequential band matrix in the spaces of convergent and null sequences, Advances in Difference Equations 2014:163, 18 pages.
  • Candan, M., 2014. Almost convergence and double sequential band matrix, Acta Math. Scientia, 34, (2), 354–366.
  • Candan, M. and Kayaduman, K., 2015. Almost Convergent sequence space Reproduced By Generalized Fibonacci Matrix and Fibonacci Core, British J. Math. Comput. Sci. 7, (2), 150-167.
  • Candan, M., 2018. A New Outlook for Almost Convergent Sequence Spaces, Cumhuriyet Sci. J. 39, (1), 34-46.
  • Duran, J. P., 1972. Infinite matrices and almost convergence, Math. Z. 128, 75-83.
  • Ganie, A. and Sheikh, N. A., 2013. On some new sequence spaces of non-absolute type and matrix transformations, Egyptian Mathematical Society, 21, 108-114.
  • Jarrah, A. M., and Malkowsky, E., 1990. BK- spaces, bases and linear operators, Ren. Circ. Mat. Palermo, 2, (52), 177–191.
  • Karaisa, A. and Özger, F., 2015. Almost difference sequence spaces reproduced by using a generalized weighted mean, J. Comput. Anal. and Appl. 19, (1), 27–38.
  • Kayaduman, K. and Şengönül, M.,(a) 2012. On the Riesz almost convergent sequence space, Abstr. Appl. Anal. 2012, article ID: 691694, 18 pages.
  • Kayaduman, K. and Şengönül, M., (b) 2012. The space of Cesaro almost convergent sequence and core theorems, Acta Mathematica Scientia, 6, 2265–2278.
  • King, J. P., 1966. Almost summable sequences, Proc. Amer. Math. Soc. 17, 1219 -1225.
  • Kirisçi, M., 2012. Almost convergence and generalized weighted mean, AIP Conf. Proc, 1470,191–194.
  • Kirisçi, M., 2014. Almost convergence and generalized weighted mean II, J.Ineq. and Appl., 1, 93, 13pages.
  • Lorentz, G. G.,1948. A contribution to the theory of divergent sequences, Acta Mathematica, 80, 167-190.
  • Móricz, F. and Rhoades, B. E., 1990. Some characterizations of almost convergence for single and double sequences. Publ. Inst. Math Nouv S`er, 48, (62), 61–68.
  • Öztürk, E.,1983. On strongly regular dual summability methods, Commun. Fac. Sci. Univ. Ank. Series: A_1, Math., Stat. 32, 1-5.
  • Sıddıqi, J. A., 1971. Infinite matrices summing every almost periodic sequences, Pacific J. Math, 39, (1), 235–251.
There are 26 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Gülsen Kılınç 0000-0002-9657-2577

Publication Date April 15, 2020
Submission Date October 29, 2019
Acceptance Date January 9, 2020
Published in Issue Year 2020

Cite

APA Kılınç, G. (2020). ∆_u^λ Matrisi Yardımıyla Tanımlanan Yeni Bir Hemen Hemen Yakınsak Dizi Uzayı Üzerine. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 10(2), 321-329. https://doi.org/10.17714/gumusfenbil.639476